Show all steps necessary to verify the trigonometric identity:
1 - 2cos^2x = 2sin^2x - 1
Answers
Step-by-step explanation:
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Using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.
The given trigonometric identity is 1-2cos²x = 2sin²x-1.
What are trigonometric identities?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation. There are various distinct trigonometric identities involving the side length as well as the angle of a triangle.
Using trigonometric identity sin²θ+cos²θ=1
Here, 1-2cos²x = 2sin²x-1
⇒ 1+1=2sin²x+2cos²x
⇒ 2=2(sin²x+cos²x)
⇒ 2=2(1)
⇒ 2=2
LHS=RHS
Therefore, using trigonometric identity sin²θ+cos²θ=1, the given identity is proved.
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Related Questions
Sam gets paid a set rate in his allowance for making his bed every morning. His rate is $0.50 earned for every morning that he makes his bed.
Let n represent the number of days Sam makes his bed.
Let t represent the total amount earned, in dollars.
Which graph shows the amount of money that Sam earned when he made his bed over the course of 8 days?
Answers
Answer:
bottom graph of left picture
Step-by-step explanation:
For each day he makes his bed, he earns $0.50
In 1 day he earns $0.50
In 2 days he earns $1.00
In 3 days, he earns $1.50
...
In 8 days, he earns $4.00
Look in the 4 graphs.
Which graph has the following points, (1, 0.5), (2, 1), 3, 1.5), ... , (8, 4)?
It is the second graph (bottom graph of left picture.)
What is the surface area of this figure?
Enter your answer in the box.
ft²
Complex solid composed of a triangular prism and a rectangular prism. The triangular prism is centered on the top of the rectangular prism. The rectangular prism bottom face is labeled 18 ft and 6 ft. The height of the rectangular prism is labeled 9 ft. The triangular base has an altitude drawn and labeled 8 ft. The sides of the triangle are labeled 10 ft, 10 ft, and 12 ft. The height of the triangular prism is 6 ft.
Answers
The total surface area of the figure is 862ft²
How to calculate the surface area of a figureThe composite figure is made up of a pyramid and prism
Surface area of pyramid = 2(13*9) + (10*9) + (10*12)
Surface area of pyramid = 234 + 90 +120
Surface area of pyramid = 444ft²
For the rectangular prism
Surface area = 2(11*9) + 2(10 * 11)
Surface area = 198 + 220
Surface area = 418ft²
Surface area of figure = 444 + 418
Surface area of figure = 862ft²
Hence the total surface area of the figure is 862ft²
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Solve the inequality -28n < 7.
Answers
Answer:
n > -1/4
Step-by-step explanation:
-28n < 7
Divide by -28 on both sides
-28/-28n < 7/-28
Flip the inequality symbol when dividing by a negative number.
n > -7/28
which simplifies to
n > -1/4
Answer:
n greater than or equal to -1/4
Step-by-step explanation:
The student body of 24 students
wants to elect a president, minister
of Arts, minister of PE department,
and minister of Science. How many
different arrangements are there?
Answers
There are 10,626 ways of arranging the required offices from a body of 24 students.
What is combination?
Combination deals with the way in which a arrangement can be made from a particular lot. In this case, we want to select a president, minister of Arts, minister of PE department, and minister of Science from a body of 24 students.
Hence;
24C4 = 24!/4! (24 - 4)! = 24!/4!20!
So;
24 * 23 * 22 * 21 * 20!/20! * 4 * 3 * 2*1
= 24 * 23 * 22 * 21 / 4 * 3 * 2*1
= 10,626 ways
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Kristen and Ben are making a poster that is 1 1/3 yard by 2 1/3 yard. What is the area of the poster?
A. 1 1/9 yd2
B. 3 1/9 yd2
C. 1 1/3 yd2
D. 9 1/3 yd2
Answers
Answer:
B
Step-by-step explanation:
[tex]1\frac{1}{3}\times2\frac{1}{3}\\= \frac{4}{3}\times\frac{7}{3}\\= \frac{28}{9}\\= \frac{27+1}{9}\\=\frac{27}{9}+\frac{1}{9}\\=3+\frac{1}{9}\\=3\frac{1}{9}[/tex]yd²
The table shows several points for function h(x). A 2-column table with 6 rows. Column 1 is labeled x with entries 0, 3, 6, 9, 12, 15. Column 2 is labeled h (X) with entries 1, 6, 12, 2, 8, 9. Which point is on the graph of the inverse function h–1(x)? (0, 1) (6, 3) (9, –15) (12, –8)
Answers
Answer:
B
Step-by-step explanation:
Ed2021
what two numbers add to 6 and multiply to -5?
Answers
Then the answer is -2 and -3
7th grade math help me plzzz
Answers
Answer:
42
Step-by-step explanation:
x+3y=15 what is the slope
Answers
Answer:
slope = -1/3
Step-by-step explanation:
x+3y=15
-x 3y=-x+15
divide by 3 y= -1/3x -5
which statement best describes the set 14 16 18 20 22
Answers
Answer:
They are adding 2 by each number.
A set of numbers is a group of numbers that are related in one way or the other. The statement that best describes the set is:
The set of even numbers from 14 to 22
Given that:
[tex]Set = 14\ 16\ 18\ 20\ 22[/tex]
From the above set of numbers, we have the following observations
All numbers are evenThe difference between consecutive numbers is 2So, we can describe the set using the following statement:
The set of even numbers from 14 to 22
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Consider the line y=2/5-4/3x what is the slope of a line perpendicular to this line
Answers
The product of the slopes of this line and the line perpendicular to it is equal to -1.
Note that the slope if the coefficient of x.
Let
[tex] \alpha [/tex]
be the slope of the given line.
Let
[tex] \beta [/tex]
be the slope of the line perpendicular to it.
I can therefore say,
[tex] \alpha \times \beta = - 1[/tex]
[tex] \frac{ - 4}{3} \times \beta = - 1[/tex]
[tex] \beta = \frac{ - 1}{ \frac{ - 4}{3} } [/tex]
[tex] \beta = \frac{ - 3}{ - 4} = \frac{3}{ 4} [/tex]
The slope is 3/4
What is the missing base of 9=____ to the power of 2?
Answers
Answer: 3
Step-by-step explanation:
Let x be the missing base. In this case, base to the power of 2 means this number x times itself will equal 9.
9 = [tex]x^{2}[/tex]
[tex]\sqrt{9}[/tex] = [tex]\sqrt{x^{2} }[/tex] [use square root to cancel the power of 2].
[tex]\sqrt{9}[/tex] = x
x = 3
Check: [tex]3^{2}[/tex] = 3 x 3 = 9
Find the area of the parallelogram ABCD
А
B
12 cm
-10 cm-
C
D
-30 cm
Answers
Answer:
I think it is 3600
Step-by-step explanation:
What happens if I fail a state test in the 9th grade?
Answers
Answer:
You will be remembered as a bad student who failed a state test in 9th grade!
Hope it helps!
Answer:
It depends on the grade or school some schools let you retake the test if you fail it you might fail that class and take the same class for 10th
Step-by-step explanation:
An archer hits a target 50% of the time. What is the experimental probability that the archer hits the target exactly four of the next five times?
Answers
Answer:
40/50
Step-by-step explanation:
That’s the probability of him hitting them
Answer:
5/32 or 15.625
Step-by-step explanation:
I don't remember how I got the answer but it was just in my notes as the answer so yea. :]
A grocery store sells four different sizes of a popular brand of corn flakes. For the past few years the proportion of boxes they sell of each size has been quite stable: 10% Small, 15% Medium, 60% Large, and 15% Jumbo. They decide to change the pricing of the four sizes and want to see if this changes the proportion of boxes they sell of each size. To test this, a few weeks after changing the prices they take a simple random sample of 120 transactions involving corn flakes and count how many boxes of each size were sold. Here are the results:
Observed number of boxes sold for each box size
Small Medium Large Jumbo
8 24 61 27
Required:
a. We wish to carry out a test of significance to see if the distribution of sizes of cereal boxes soldhas changed. State the null and alternative hypotheses for this test.
b. Find the expected counts for each size box under the assumption that the null hypothesis is true.
Answers
The sale of the four different sizes is an illustration of the Goodness of Fit Tests
The expected counts for each size box are 0.8, 3.6, 36.6 and 4.05 respectively
The null and the alternate hypothesesThe null hypothesis is always represented by the equality sign i.e. 0 change or no change.
While the alternate hypothesis is always represented by an inequality.
So, the null and the alternate hypotheses are:
Null hypothesis; H0 : The distribution of sizes of all boxes sold of this brand of cereal did not change when the prices changed.Alternate hypothesis; Ha: The distribution of sizes of all boxes sold of this brand of cereal changed when the prices changed.The expected counts for each size boxThis calculated as:
E(x) = np
So, we have:
Small = 8 * 10% = 0.8
Medium = 24 * 15% = 3.6
Large = 61 * 60% = 36.6
Jumbo = 27 * 15% = 4.05
Hence, the expected counts for each size box are 0.8, 3.6, 36.6 and 4.05 respectively
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A circle has a radius of 11 mm. What is its circumference?
Answers
Answer:
≈ 69.08mm
Step-by-step explanation:
The circumference of a circle can be found with the formula:
[tex]C=2$\pi$r[/tex], where r is the radius of the circle.
Let's solve for the circumference.
[tex]2*3.14=6.28[/tex]
[tex]6.28*11=69.08[/tex]
Therefore, the circumference is 69.08
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6th grade math I mark as brainliest
Answers
Answer:
1,3,5
Step-by-step explanation:
1-The first one because you move to the left one place value
2-the value is not 10 times greater it is ten times smaller because it moves to the right one value
3-yes, the 8 is ten times greater because it moved to the right one place value
4-This is not true because if it was 1/10th the value it needs to be ten times smaller, not ten times greater
5- this is true because it moves to the right by one place value
6- this is not true because it is ten times greater not ten times smaller
Hope this helps you out!
Which situation is represented by the equation 12 x 6 =
Answers
Answer:
60
Step-by-step explanation:
A man purchase 5 dozen banana , find equation to find total number of banana and how many banana he have.
Total number of banana = 12 x 6
Total number of banana = 60
which statement are true about the following diagram as labeled
Answers
Answer: Triangle ADB is congruent to CBD
Step-by-step explanation:
S1: Try to measure the sides to look alike.
S2: Compare your answers to someone in your class!!!
(6x-1) = (5x+28)
X=?
Answers
x = 29
Answer:
x = 29
Step-by-step explanation:
(6x-1) = (5x+28)
or, 6x-1 = 5x+28
or, 6x-5x = 28+1
or, x = 29
Find the rule to solve for N. X,5,6,n,10 Y,20,24,32,40
Answers
Answer:
Step-by-step explanation:
Consider what y values you are getting by letting x = 5 and then letting x = 6.
when x = 5 , y = 20
y = m*5
20 = m*5 Divide by 5
20/5 = m/5
4 = m
when x = 6 y = 24
y = mx
24 = m*6 Divide by 6
24/6 = m
m = 4
So now we can be sure of our solution for x when y = 32
y = m*n
32 = 4*n Divide both sides by 4
32/4 = 4*n/4
n = 8
Answer: n = 8
Through the points (-4,2) and (-7,-7) hurrrryyy!!!!!!
Answers
Answer:
(-9,4)
Step-by-step explanation:
Please help I need an answer quick too!!!!
Answers
Sjjsnsbsns
Winston has just gone grocery shopping. The mean cost for each item in his bag was $3.24. He bought a total of 5 items, and the prices of 4 of those items are listed below:
$4.55,$2.53,$2.82,$4.66
Determine the price of the 5th item in his bag.
Answers
Answer:
$1.26
Step-by-step explanation:
total: 16.2 (3.24 * 5)
4.55 + 2.53 + 2.82 + 4.66 = 14.56
16.2 - 14.56 = 1.26
The price of the fifth item in W's bag is $1.55 if the mean price of all five items is $3.24.
A mean is one of the measures of central tendencies and is the average value of a group of observations. It is the ratio of the sum of all observations to the total number of observations.
The prices of the 4 items out of the 5 items W has bought are given as follows:
$4.55, $2.53, $2.82, $4.66
It is also given that the mean cost for each item is $3.24.
Let the price of the fifth item be x, then according to the question;
[tex]\dfrac{ 4.55+ 2.53+2.82+4.66+x}{5} = 3.24\\14.65 + x = 3.24 \times 5\\14.65 + x = 16.2\\x = 1.55[/tex]
Therefore, the price of the fifth item in the bag is $1.55.
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If three angles of a triangle are "(3x - 2) degrees, (8x - 5) degrees, and (7x+7) degrees", then what does "x" equal?
Answers
Answer:
10
Step-by-step explanation:
The sum of the measures of the angles of a triangle.is 180 degrees, so:
3x-2+8x-5+7x+7=180
18x=180
x=10
Pls help there will be pic if u click
Answers
Answer:
$6.30
Step-by-step explanation:
A sharpener is 0.90 in dollars, so 3*0.9 is 2.7. 10-2.7=6.3, so the answer should be $6.30
You are paying with $10.
$10-$2.70=$7.30.
You are getting $7.30 for change.
2.8x = -9.24
A. 12.04
B. -0.3030
C. -3.3
D. 12.04
Please helppp
Answers
Answer:
Choice c, 3.3
Step-by-step explanation:
To find out the vaule of X, we have to divided -9.24 by 2.8. We have to divided because when X and next to a number, it means to multiply, and the opposite of multiplication is division. To double check to determine whether or not the answer is correct, simply multiply -3.3 by 2.8 and you will get -9.24.
How many 1/4 cup servings are in 3 cups of chololate?
Answers
Answer:
The answer is 12. In 3 cups of chocolate, there are 12 1/4 cup in them.
Step-by-step explanation:
each 1 cup had four 1/4 cup in them. So 4 times 3 cups is 12.
There are 12 servings of 1/4 cup in 3 cups of chocolate.
The term "serving" typically refers to a specified portion or amount of food or drink that is recommended or commonly consumed at one time. It helps in providing a standard measurement for nutritional information and portion control.
To determine the number of 1/4 cup servings in 3 cups of chocolate, we need to calculate the total number of 1/4 cup servings that can be made from the given amount.
1. One cup is equal to 4 quarters (1 cup = 4 × 1/4 cup).
2. To find the number of 1/4 cup servings in 3 cups, multiply 3 cups by the conversion factor (4 × 1/4 cup) for each cup.
3 cups × (4 × 1/4 cup) = 3 cups × 1 cup = 3 cups
Therefore, there are 3 * 4 = 12 servings of 1/4 cup in 3 cups of chocolate.
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Hep math math math math
Answers
Answer:
c
Step-by-step explanation:
basic theory, can't explain further.
Answer: y=6
Step-by-step: 2(−6)+3=18 distributed into 2−12+3=18
Next, Combine Like Terms.
2−12+3=18
5−12=18
Wait oh, you wanted the. Oh. Well the distribution of it is 2y-12+3y=18. Sorry!