Which of the expressions in Exercises are defined, and whichare not? Give reasons for your answers.51. a. tan-1 2                            b. cos-1 2

Q: Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not…

A: Solution : The objective is to simplify the given expression

Q: Determine whether the statement is true or false Given that cos(2t) = 2 cos²(t) – 1, it follows that…

A:

Q: For Exercises, 15–20, find the exact value of the expression. 2 tan 15° 16. 2 tan 67.5° 17. 2sin-cos…

A: 15. 2 tan67.5o1-tan267.5osolution(15)tan2x=2tanx1-tan2x2 tan67.5o1-tan267.5o=tan(2×67.5o)2…

Q: Which is the simplified form of the expression t. 1-cos(5A), 1+cos(5A)

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Q: Which of the following is equivalent to expression cosh?u- sinh²u? (A) 2e-u (B) cosh2u 2e" D none of…

A: Using the formulas of coshx and sinhx

Q: Can you please answer this question

A: Write tanx as sinx/cosx, then assume z=cosx and find dx.

Q: 6. 10 What is the value of tan x? O A. O B. 4 C.

A: As tan x=Opposite/adjacent       tan x =8/6  So  tan x=4/3

Q: Pls help ASAP

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Q: 30. When < 0 < 3, which of the following could possibly be tan 0? о (а) —8 • (b) - (c) 0 (d) 1

A: According to the problem, we have

Q: - TT < x < TT; function, f(x) = cos(x/2)

A:

Q: Complete the sentence below. The least positive number x for which cos x=0 is (Type an exact answer,…

A: Use the fact that the value of cos π2=1.

Q: Which of the following is equivalent to expression cosh?u- sinh?u? (A 2e-u B none of the given…

A: Let's find.

Q: Which of the following is equivalent to expression cosh?u- sinh?u? A 2e-u В 1 2eu cosh2u E none of…

A: We have to find

Q: What value of x will make sinx= -? 2 (A none of the given choices 3 TT - 2 - 4 TT 6 B.

A: Given:- sinx = -1/2 To find :- value of x

Q: Which of the following is equivalent to 4 sin? x cos? x- 1? O - sin 2x | O cos? 2x O- cos? 2x | O…

A: Which of the following is equivalent to  4sin2x cos2 -1 ?

Q: Which of the following is equivalent (cos x + sin x)(cos x – sin x) 1. sin? 2x

A: We have to choose the equivalent to

Q: Which of the expressions in Exercises are defined, and whichare not? Give reasons for your…

A: a) cot-1-12b) cos-1-5

Q: (6) For each statement below, determine whether the equality is correct, and explain your solution.…

A: (a) Consider the given equation: sinsin-1x=x This is true for all the function values because domain…

Q: 20. Simplify the expression o con z- sin z-1 tan z O - sec? z O - tan? z O sec? z

A: We have to simplify the following expression -  cos2x-1sin2x-1

Q: Determine the value of sin t when t = 5π, -2π, 17π/2,-13π/2.

A: we have to find the value of sin t when t = 5π, -2π, 17π/2, -13π/2.

Q: Which of the following expressions correctly determines the value of cos ZC? A 10 C

A: Given that :- a=8 b=10 cos∠C=?

Q: Which is tan(A+B) if sin.A = -- with 270° <A< 360° and if cos B = - with 90° < B < 180°? 13 56 56 H…

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Q: Which of the expressions in Exercises are defined, and whichare not? Give reasons for your…

A: The values present in the inverse trigonometric functions help to check the validity of the…

Q: Which of the following equations could not be used to find the value of x? 23.6° 12 30 66.4 Hint:…

A:

Q: Which of the following is equivalent to expression cosh²u- sinh?u? A none of the given choices B…

A: Given that, the expression is following, cosh2x - sinh2x We have to simplify this expression and…

Q: Which of the following expressions correctly determines the value of COS ZA? В 8 A 10 C 82 + 102 +…

A:

Q: Simplify the 18ll8WIng expressIons. a) cos?x (tan2x + 1) b) v1 - sin a V1+ sin a

A: To simplify the expressions

Q: Which is cos 2o if sin o= - and 180° < o< 270°? 13 13 5 C 5 13 5 13 B 13 D 5

A:

Q: alent expr

A: Here we have to find sinK=?

Q: Which of the following is not true? a) cos?t+ sin²t = 1 b) csc²t - cot2t=1 c) cos?t- sim²t = 1 d)…

A:

Q: Which of the following statements is true? Lun -1(2) dr= A tan +C 1+x? 9* +C 5ln (9) B © Jcon…

A: We have to find which statements is true.

Q: Write the expression as an algebraic expression in u, u>0. cos [tan-¹)]

A: Given: Simplify as an algebraic expression costan-1u4 in u, u&gt;0 For inverse function tan-1x=θ If…

Q: Which of the following is equivalent to expression cosh?u- sinh²u? A) none of the given choices B 1…

A:

Q: Which of the following expressions is equal to the given expression below? 1-c O s 8x 1+c oS 4x V1 –…

A: 1-cos8x1+cos4x

Q: Which of the following expressions correctly determines the value of cos ZA? В 8. A 10 C 82 + 102 +…

A:

Q: PROVE THE GIVEN 2n sin? (V5 - 1) sin? 3 8

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Q: Which set of values is the solution for (2 sin x + 1)(cosx- 1) = 0,0s xs 27 ? 7 11 a) 1, -7, 6. 7.…

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Q: Find the value of tan X. 18. 20 Y 15 25 Oa) 3/4 O b) 4/3 Oc) 5/3 O d) 3/5

A: To find The value of tanx from the given right angled triangle

Q: 5. Simplify the expression cos" a–1 sin a-1 sec? a O - sec? æ O tan? x O - tan? z

A:

Q: Which of the following is equivalent to expression cosh²u- sinhu? A none of the given choices B 1…

A: The given expression, cosh2u-sinh2u

Q: Which of the following is equivalent to expression cosh?u - sinh?u? 1 2e" © none of the given…

A:

Q: Which of the following values of Y will the expression sin y 1- sin? y be undefined? 37T 2 None of…

A: Topic:- calculus

Q: What is the approximate value of tan (3)? O-3.078 O 0.033 O 1.083 O2.468

A:

Q: tanwdw The is equal to 1 – tan?w A. In (Vsec2w) + C B. In (Vsec2w) +C C. In (Vsec2w) + C D. In…

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Q: Which equations are true? Select all that apply. C 3 A 4 O cos(A) O cos(A) O cos(A) O sin(A) Osin(A)…

A: In a right angle triangle with respect to angle θ, the sine and cosine function is defined as, sin…

Q: Which of the following expressions is equivalent to -? Cos a cos a 1-cos a a. c. 1- sin? 1+cos a d.…

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Q: On the domain of (-27, 27), for which of the following values of x will sin x = csc x? Choose all…

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Q: Cannot solve

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Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.