Considering only the values of [tex]\beta[/tex] for which [tex]\sin \beta \tan \beta \sec \beta \cot \beta[/tex] is defined, which of the following expressions is equivalent to [tex]\sin \beta \tan \beta \sec \beta \cot \beta[/tex]?

a. [tex]\sec \beta \cot \beta[/tex]
b. [tex]\tan \beta[/tex]
c. [tex]\cot \beta \tan \beta[/tex]
d. [tex]\tan \beta \csc \beta \sec \beta[/tex]

Answers

Answer 1

[tex]\large\boxed{Answer:}[/tex]

We will use trigonometric identities to solve this. I will use θ (theta) for the angle.

First of all, we know that cotθ = 1/tanθ. This is a trigonometric identity.

We can replace cotθ in the expression with 1/tanθ.

[tex]sin\theta tan\theta sec\theta \frac{1}{tan\theta}[/tex]

Simplify: 1/tanθ * tanθ = tanθ/tanθ = 1

So now, we have:

[tex]sin\theta sec\theta[/tex]

Next, we also know that secθ = 1/cosθ. This is another trigonometric identity.

We can replace secθ with 1/cosθ in our expression.

[tex]sin\theta \frac{1}{cos\theta}[/tex]

Simplify:

[tex]\frac{sin\theta}{cos\theta}[/tex]

Our third trigonometric identity that we will use is tanθ = sinθ/cosθ.

We can replace sinθ/cosθ with tanθ.

Now we have as our final answer:

[tex]\large\boxed{b.\ tan\theta}[/tex]

Hope this helps!

Answer 2

Answer:

[tex] \huge \boxed{ \boxed{ \red{b) \tan( \beta ) }}}[/tex]

Step-by-step explanation:

to understand thisyou need to know about:trigonometryPEMDASgiven:[tex]\sin \beta \tan \beta \sec \beta \cot \beta[/tex]tips and formulas:[tex] \tan( \theta) = \dfrac{ \sin( \theta) }{ \cos( \theta) } [/tex][tex] \cot( \theta) = \dfrac{ \cos( \theta) }{ \sin( \theta) } [/tex][tex] \sec( \theta) = \dfrac{1}{ \cos( \theta) } [/tex]

let's solve:[tex] \sf rewrite \: \tan( \beta ) \: as \: \dfrac{ \sin( \beta ) }{ \cos( \beta ) } : \\\sin (\beta ) \cdot\frac{ \sin( \beta ) }{ \cos( \beta ) } \cdot \sec (\beta ) \cdot\cot (\beta)[/tex][tex] \sf rewrite \: \sec( \beta ) \: as \: \dfrac{1 }{ \cos( \beta ) } : \\\sin (\beta) \cdot\frac{ \sin( \beta ) }{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot\cot (\beta)[/tex][tex] \sf rewrite \: \cot( \beta ) \: as \: \dfrac{ \cos( \beta ) }{ \sin( \beta ) } : \\\sin (\beta) \cdot\frac{ \sin( \beta ) }{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot \: \dfrac{ \cos( \beta ) }{ \sin( \beta ) }[/tex][tex] \sf \: cancel \: sin : \\\sin (\beta) \cdot\frac{ \cancel{\sin( \beta ) }}{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot \: \dfrac{ \cos( \beta ) }{ \cancel{\sin( \beta ) }} \\ \sin (\beta) \cdot\frac{ 1 }{ \cos( \beta ) } \cdot \frac{1}{ \cos( \beta ) } \cdot \: \cos( \beta ) \\ [/tex][tex] \sf cancel \: cos : \\ \sin (\beta) \cdot\frac{ 1}{ \cos( \beta ) } \cdot \frac{1}{ \cancel{ \cos( \beta )} } \cdot \: \cancel{ \cos( \beta ) } \\ \\ \sin( \beta ) \: \cdot \: \dfrac{ 1 }{ \cos( \beta ) } [/tex][tex] \sf \: simplify \: multipication : \\ \dfrac{ \sin( \beta ) }{ \cos( \beta ) } [/tex][tex] \sf use \: \frac{ \sin( \beta ) }{ \cos( \beta ) } = \tan( \beta ) \: identity : \\ \therefore \: \tan( \beta ) [/tex]


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x = 4

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Step-by-step explanation:

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Answer:

Th answer to the first question is 18+6=24 the answer to the second question is 9 weeks

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A
B
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Answer:

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Step-by-step explanation:

Answer:

D

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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I'm only sure about the second one

Answer:

Yes

Step-by-step explanation:

(2, 1) is a solution to the given system of linear equations.

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Improper Fraction =75/14
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Which of the lines below has a negative slope?
A
B
6
-5
15
6
10
5
D
5
5

Answers

Well, negative slope has the word negative in it right? So, it will be the negative number. Answer: -5 (negative 5)

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here are the answers btw:

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Answers

Step-by-step explanation:

7m - 10 - 4m + 3

3m-7

Hope it helps

7m-10-4m+3
=7m-4m-10+3
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What is the explicit rule for the arithmetic sequence? 20.5, 16, 11.5, 7, 2.5, ...

Answers

Answer:

To determine the explicit rule for the arithmetic sequence of 20.5, 16, 11.5, 7, 2.5, ..., the following logical reasoning must be performed:

20.5 - 16 = 4.5

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Answers

Answer:

A. 135% of 85

Step-by-step explanation:

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Answers

Answer:

180=2x+ 24( angles opposite to equal sides)

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Step-by-step explanation:

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What Is an Isosceles Triangle?

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

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Given data ,

Let the triangle be represented as ABC

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Find the value that makes the proportion true.

Answers

Answer:

can not see page

Step-by-step explanation:

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Answer:

707 bags of sand

Step-by-step explanation:

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Answers

Answer:

the answer is B

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Olivia has 1/2 pound of raisins. She plans to eat them for snacks over the next 6 days. If she eats the same amount each day, What fraction of a pound of raisins will she eat each day

Answers

Answer :

1/12

Step by step :

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Number of days : 6

Pounds of raisins she will eat every day :

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When a certain kind of bacterium takes a step, it moves 3 x 10^-7 meters. When
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Answers

Answer:

Step-by-step explanation:

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Answers

Answer:

9a^2 - 6a

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Simplify the expression:
2n + 10(9 + 4n)

Answers

Answer:

42n+90

Step-by-step explanation:

Answer: 42n+90
Explaination:

2
n
+
10
(
9
+
4
n
)
Distribute:
=
2
n
+
(
10
)
(
9
)
+
(
10
)
(
4
n
)
=
2
n
+
90
+
40
n
Combine Like Terms:
=
2
n
+
90
+
40
n
=
(
2
n
+
40
n
)
+
(
90
)
=
42
n
+
90

Find n(E), given that n(C×E)=18 and C={4,5,6}

Answers

Answer:

ncx(2.718282)=18;c=456

ncx(2.718282)=18;c=456

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Step-by-step explanation:

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Answers

Answer:

f(-2) = 54

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

f(x) = 3x(x² + 4x - 5)

f(-2) is x = -2

Step 2: Evaluate

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Answers

Answer:

B

Step-by-step explanation:

how many 1/2's in 4? thats how many bows so 4 ÷ 1/2

Answer:

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Find the slope of the line that passes through the two points. (-3, -4), (6, 8)

Answers

Answer:

Step-by-step explanation:

let (x1 , y1) = ( - 3, - 4) and (x2 , y2) = ( 6 , 8)

Slope (m)

= y2 - y1 / x2 - x1

= 8 + 4 / 6 + 3

= 12 / 9

= 4/3

Paul has some money in his wallet, all in $1 bills. He buys a hat and has $6 left, as shown in
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Enter your answer in the box.

Answers

Answer:

we need to see the model

Step-by-step explanation:

model please

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Answers

Answer:

17

Step-by-step explanation:

180 - 5 - 5 = 170 : 2 = 85 : 5 = 17

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Answers

Answer:

117

Step-by-step explanation:

There are 60 minutes in each hour, and to find how many minutes there are in 3 hours you would have to multiply 3 x 60.

3 x 60 = 180

To find 65% of 180 you can use the equation

65 x 180/100

65 x 180 divided by 100 is 117.

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