Answers
Answer:
[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]
[tex]\cot(x)+\tan(x)[/tex]
[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]
[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{1}{\cos(x)}][/tex]
[tex]\csc(x)[\sec(x)][/tex]
[tex]\csc(x)[\csc(\frac{\pi}{2}-x)][/tex]
[tex]\csc(x)\csc(\frac{\pi}{2}-x)[/tex]
Step-by-step explanation:
I'm going to use [tex]x[/tex] instead of [tex]\theta[/tex] because it is less characters for me to type.
I'm going to start with the left hand side and see if I can turn it into the right hand side.
[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]
I'm going to use a cofunction identity for the 2nd term.
This is the identity: [tex]\tan(x)=\cot(\frac{\pi}{2}-x)[/tex] I'm going to use there.
[tex]\cot(x)+\tan(x)[/tex]
I'm going to rewrite this in terms of [tex]\sin(x)[/tex] and [tex]\cos(x)[/tex] because I prefer to work in those terms. My objective here is to some how write this sum as a product.
I'm going to first use these quotient identities: [tex]\frac{\cos(x)}{\sin(x)}=\cot(x)[/tex] and [tex]\frac{\sin(x)}{\cos(x)}=\tan(x)[/tex]
So we have:
[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]
I'm going to factor out [tex]\frac{1}{\sin(x)}[/tex] because if I do that I will have the [tex]\csc(x)[/tex] factor I see on the right by the reciprocal identity:
[tex]\csc(x)=\frac{1}{\sin(x)}[/tex]
[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
Now I need to somehow show right right factor of this is equal to the right factor of the right hand side.
That is, I need to show [tex]\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}[/tex] is equal to [tex]\csc(\frac{\pi}{2}-x)[/tex].
So since I want one term I'm going to write as a single fraction first:
[tex]\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)}[/tex]
Find a common denominator which is [tex]\cos(x)[/tex]:
[tex]\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}[/tex]
[tex]\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}[/tex]
[tex]\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}[/tex]
By the Pythagorean Identity [tex]\cos^2(x)+\sin^2(x)=1[/tex] I can rewrite the top as 1:
[tex]\frac{1}{\cos(x)}[/tex]
By the quotient identity [tex]\sec(x)=\frac{1}{\cos(x)}[/tex], I can rewrite this as:
[tex]\sec(x)[/tex]
By the cofunction identity [tex]\sec(x)=\csc(x)=(\frac{\pi}{2}-x)[/tex], we have the second factor of the right hand side:
[tex]\csc(\frac{\pi}{2}-x)[/tex]
Let's just do it all together without all the words now:
[tex]\cot(x)+\cot(\frac{\pi}{2}-x)[/tex]
[tex]\cot(x)+\tan(x)[/tex]
[tex]\frac{\cos(x)}{\sin(x)}+\frac{\sin(x)}{\cos(x)}[/tex]
[tex]\frac{1}{\sin(x)}(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)(\cos(x)+\sin(x)\frac{\sin(x)}{\cos(x)})[/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)}{\cos(x)}+\sin(x)\frac{sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos(x)\cos(x)+\sin(x)\sin(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}][/tex]
[tex]\csc(x)[\frac{1}{\cos(x)}][/tex]
[tex]\csc(x)[\sec(x)][/tex]
[tex]\csc(x)[\csc(\frac{\pi}{2}-x)][/tex]
[tex]\csc(x)\csc(\frac{\pi}{2}-x)[/tex]
Related Questions
1. Find the slope and the y-intercept
of the graph of the linear equation.
y = -7x + 2
A) slope: -3; y-intercept: 2
1
B) slope: 2; y-intercept: -7
C) slope: -7; y-intercept: 2
D) slope: 2; y-intercept: -7
Answers
Answer:
c) slope: -7 ; y-intercept: 2
Step-by-step explanation:
Note the slope intercept form:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
Note in this case:
y = (-7)x + 2
y = y
m = -7
x = x
b = 2
c) slope: -7 ; y-intercept: 2 is your answer.
~
some one help me with this the highlighted one is the problem
Answers
atomic mass number
atomic symbol
periodic table
groups
8
periods
7
amphoteric line
transition metals
non-metals
other metals
bromine
dull
electricity
magnets
-12x + 4y- 6y + 10x - 25 5x - 2(x - 12)
Answers
Answer:
=−259x−2y+24
Step-by-step explanation:
Distribute:
=−12x+4y+−6y+10x+−255x+(−2)(x)+(−2)(−12)
=−12x+4y+−6y+10x+−255x+−2x+24
Combine Like Terms:
=−12x+4y+−6y+10x+−255x+−2x+24
=(−12x+10x+−255x+−2x)+(4y+−6y)+(24)
=−259x+−2y+24
Answer:
=−259x−2y+24
Hope this helps emmy! or emma
(sorry I like calling you emmy)
Question 6
Find the slope of the line that passes through the pair of points.
(-3, 2), (7, 2)
Answers
Answer:
Slope = 0
Step-by-step explanation:
Given the pair of points: (-3,2) (7,2)
Slope formula: y2-y1/x2-x1
2-2/7-(-3) = 0/10
0/10 = 0
I need help on how to get the answer too number 27.
Answers
3^2 + 8^2 = c^2
9 + 64 = c^2
73 =c^2
take the square root of each side
c= 8.544
Sketch a graph of the function y = (x + 6)(x- 4)
Answers
Step-by-step explanation:
eyoaekzgzegkegkzEGKegkzegkzkegzegkzegkzhekzkehskzFegkzkegzgkzejfszfjsjwfJwfUr
Help ASAP!!! Question in pic! Will give brainliest!
Answers
Answer:
It is 15.
Step-by-step explanation:
We know the common difference is 2 right?
7
9
11
13
15
Those are 5 times, so its 15.
(Can I get Brainliest)
Answer:
15Step-by-step explanation:
because the common difference is 2, it would look like this: 7,9,11,13,15
Surface area question:
Answers
Answer:
190π (not part of the answer choices)
Step-by-step explanation:
The surface area of a cylinder can be found using the formula below:
[tex]SA=2\pi r^2+\pi dh[/tex] where [tex]r[/tex] is the radius of the base, [tex]d[/tex] is the diameter of the base and [tex]h[/tex] is the height of the cylinder.
Plug in the given values
[tex]SA=2\pi (\frac{10}{2}) ^2+\pi (10)(14)\\SA=2\pi (\frac{100}{4})+140\pi\\SA=2\pi (25)+140\pi\\SA=50\pi+140\pi\\SA=190\pi[/tex]
Therefore, although this answer isn't one of the choices, the surface area of the cylinder is 190π.
I hope this helps!
Hi can someone help me with my math homework? I just need help with number c.
Answers
Answer:
Check pdf
Step-by-step explanation:
Answer:
11/4 pints
Step-by-step explanation:
3¹/² pints of blueberries is equal to 7/2 pints
she ate 3/4pints
7/2is equal to 14/4 because we need same denominator
now we subtract
14/4-3/4
=11/4 pints is left
1. x-y=1
x+y=-5
2. x-4y=10
2x+y=2
3. -5x+y=0
x+y=6
4. y=6-2x
y=4
5. 2y=16
4x-y= 4
6. x=y -4
3x+y=12
7. y- 2x=-6
5x-y= 9
8. 3y+x= 2
y-x=-6
Answers
Answer:
what is the question write it in thecomments and ill answer
Answer:
1.) (y+1)+y=-5
2y=-6
y=-3
x+(-3)=-5
x=-2
plug in to check if it works
2.) 2(4y+10)+y=2
9y+20=2
9y=-18
y=-2
x-4(-2)=10
x+8=10
x=2
3.) -5(-y+6)+y=0
5y-30=0
5y=30
y=6
x+(6)=6
x=0
4.) 4=6-2x
-2=2x
x=-1
y=6-2(-1)
y=8
5.) 4x-(8)=4
4x=12
x=3
4(3)-y=4
12-y=4
-y=-8
y=8
6.) 3(y-4)+y=12
4y-12=12
4y=24
y=6
x=6-4
x=2
7.) 5x-2x-6=9
3x=15
x=5
5(5)-y=9
25-y=9
-y=-16
y=16
8.)3(x-6)+x=2
4x-18=2
4x=20
x=5
y-5=-6
y=-1
hope this helped :)) also make sure to plug the x and y back into both equations :))
If x = 8 units, y = 3 units, and h = 1 unit, then what is the area of the parallelogram shown above?
Answers
Answer:
8unit²
Step-by-step explanation:
The Area of a parallelogram :
Length of base * height
Length of base, x = 8 units
Height, h = 1 unit
Area = Length of base * height
Area = 8 units * 1 unit
Area = 8unit²
8x−20
Apply the distributive property to factor out the greatest common factor.
Answers
Answer: 4(2x - 5)
Step-by-step explanation:
factors of 8 : (2, 2), 2
20 : (2, 2), 5
Therefore the GCF is 2*2 = 4
8x/4 = 2x and -20/4 = -5
4(2x - 5) = 8x - 20
What is the value of x?
Answers
Answer:
B
Step-by-step explanation:
Since UV is a tangent then ∠ WUV = 90°
WZ = WU = x - 1 ( both radii of the circle ) , then
WV = x - 1 + 2 = x + 1
Using Pythagoras' identity in the right triangle
WU² + UV² = WV² , that is
(x - 1)² + (2x - 4)² = (x + 1)² ← expand factors using FOIL
x² - 2x + 1 + 4x² - 16x + 16 = x² + 2x + 1
5x² - 18x + 17 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides
4x² - 20x + 16 = 0 ← divide through by 4
x² - 5x + 4 = 0
(x - 1)(x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 4 = 0 ⇒ x = 4
But x ≠ 1 as radius x - 1 = 0
Thus x = 4 → B
9. What is the inverse of y = 10x -2?
Answers
Answer:
f(x)^-1=x-2/10
Step-by-step explanation:
Help me please this is my homework question
Answers
512 c2 so A sorry if im wrong
Answer:
384
Step-by-step explanation:
So there are 6 faces in a cube so first you need to know how big is one face then just multiply by 6 for all 6 faces. so 8*8 = 64. that means 64 is the area of one face.
then multiply that by 6 to get the total surface area.
there it is your answer 384 the 3rd option there
Help please I do not get this problem at all
Answers
Answer:
It should be 4. The ratio that AC is equal to DE at should be equal to the ratio of BE to BC. If you want an explanation I'd be happy to add one!
omg guys imagine sneezing all day and then next thing hourssss later boom you lost your voice has that ever happened to you
Answers
Answer:
no lol
Step-by-step explanation:
URGENT !!!!!!!!! Please answer correctly !!!!! Will be marking Brianliest !!!!!!!!!!!!!!!!
Answers
Answer:
slope is 15/5=3
Step-by-step explanation:
Find the area of the blue shaded figure.
25 mm
120 mm
I’m begging atp. Please help me
Answers
area of blue shaded figure = area of big circle minus small circle
radius of big circle = 60mm
area of big circle= πr² = check pic
NEED TO TURN IN NOW PLEASE HELP ME
Answers
Always happy to help!
will mark brainliest and rate 5/5
Answers
Answer:
C.) 10,240 cubic feet
Step-by-step explanation:
We have to first find the area of the base by multiplying 32 by 32. 32 * 32 is equal to 1024. Next, we multiply by the height divided by 3. 30/3 is equal to 10, so the total volume is equal to 1024 * 10, which is 10240.
helllp i really need helpp i hate math
Answers
Answer:
C) 10.92
Step-by-step explanation:
A= 1/2bh
A = 1/2(2.8)(7.8)
A= 1/2(21.84)
A = 10.92
Answer:
C. 10.92^2
Step-by-step explanation:
Area of triangles can be solved using: 1/2*b*h
1/2*2.8*7.8=10.92
Please help me out!
Evaluate 3 x 2÷4y
Answers
Step-by-step explanation:
3 x 2÷4y
3/2y
hope it helps ☺️
HELP!!!
...................
Answers
Answer:
Step-by-step explanation:
b
6x - 2x = 16 + 8
4x = 24
x = 6
2
12p^7
Two similar rectangles are shown. Which statement is true? A) The area of rectangle B is 1 3 the area of rectangle A. B) The area of rectangle B is 1 9 the area of rectangle A. C) The area of rectangle B is nine times the area of rectangle A. Eliminate D) The area of rectangle B is three times the area of rectangle A
Answers
Answer:
I think it is 19 I not really sure
Step-by-step explanation:
o work it out of my paper and I got 19
Answer: The answer to this math question about finding the statement is very true about 2 similar rectangles are being shown here below is B). B) The area of rectangle B is [tex]\frac{1}{9}[/tex] of the area of rectangle A.
Step-by-step explanation: I'm very sorry about that, but I don't have any step-by-step explanation to this math question about finding the statement is very true about 2 similar rectangles are shown here below, so anyways, I hope that my full short given answer without my given step-by-step explanation to your own math question about finding the statement is very true about 2 similar rectangles are being shown here below, please mark me as Brainliest, take care, always be safe, and have a great rest of the day and good night! :D
Sincerely,
Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
It’s due in an hour please help
Answers
What is the value of X
Answers
Answer:
11=x
Step-by-step explanation:
since the lines are parallel the distances between each section of line is proportional to each other.
5/6=(x-1)/12
multiply both sides by 12
12(5/6)=(x-1)12/12
10=(x-1)
add 1 to both sides
10+1=x-1+1
11=x
I hope that helps :)
URGENT !!!!!!!!! Please answer correctly !!!!! Will be marking Brianliest !!!!!!!!!!!!!!!!
Answers
Step by Step :
18 - 8 = 10
-15 - 10 = -25
10/-25 = -2/5
Find the value of x.
Answers
Answer:
10
Step-by-step explanation:
7x+5 = 9x -15
5 = 2x -15
2x = 20
x = 10
PLEASE HELP I DONT UNDERSTAND
Answers
Answer:
112
Step-by-step explanation:
Divide 1111 By 999 and you get 1.1121121121121
So 112 is repeating over and over in the decimal.
112 is repeated 4 times and starts to repeat again.
Hope that helps!