Which of the following is a valid step in proving the identity 1/ sin theta - sin theta  = cos 2 theta / sec theta ?   a. Multiply both sides of the equation by sin thetab. Add sin theta to both sides of the equation.c. Multiply both sides of the equation by cos  2 theta d. Write the left side as  1/ sin theta  - sin 2 theta / sin theta

Q: Which of the following equations is an identity? There is only one in the list. a) æ² + y? = r² b)…

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Q: If 90° < 0 < 180° and sin 0 = 2, find cos 20. 8 49 8 49

A: It is given that, 90°&lt;θ&lt;180° , and sinθ=27,  we have to find cos2θ=?

Q: Which of the following is equivalent to | cos(4a)sin (4x) da ? cos udu · 1 sin udu, where u = 4x…

A: The answer is found in step-2.

Q: Use the given conditions to find the exact value of the expression. 24 COs a = 25 sin a < 0, cos a…

A: The given trigonometric expression is cosα+5π6. The conditions given are cosα=2425 and sinα&lt;0.…

Q: Use the fact that 2(V6 + V2) cos- to find sin and cos 24 24

A: Given that the fact cos π12 = 146+2 To find the cos π24  and   sin π24

Q: Match each expression with the appropriate formula that would be used for simplification. sin 8x +…

A: Solution:-

Q: Solve the following for 0, in radians, where 0 <0 < 2n. -4 sin? (0) – 7 sin(0) + 7 = 0 Select all…

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

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Q: Which of the following is equivalent to 4 cos? r+ 8 sin? 2 +4 tan? x sin? 2? O 4 sec2 x O 4 tan? a O…

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Q: Solve the following. 3 ,n < A< 5 and tan B = - 2 7 0 <B < 24' 1. Given that cosA = - find: (a)…

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Q: Which expression is equivalent to sec a(1 – cos?a) for all values of a for which sec a(1 – cos²a) is…

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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: From the formula of sin (A + B), deduce the formulae of cos(A+ B) and cos (A- B).

A: To derive formula cos(A+B) &amp; cos(A-B) using formula of sin(A+B)

Q: If cos(a) = 2/3 , sin(b) = -3/5, P(a) in Q1, P(b) in Q3,  find cos2(b)

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Q: Verify the identity by following the steps below. sin(x)cot(x) cos(x) 1) Write the left-hand side in…

A:

Q: Use an addition or subtraction formula to find the exact value of cos(−π12)=√A(√B+1)4. A= B=

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Q: 1 simplifies to which of The expression che following? (a) 2 cos² 0 (b) 2 sec? e (c) 2 sin? 0 (d) 2…

A: Let the given expression be y - y = 11-sinθ+11+sinθy = 1×1+sinθ+1×1-sinθ1-sinθ1+sinθy =…

Q: 7 cos? (0) + 2 cos(0) – 7 = 0 COS

A: 7cos2θ+2cosθ-7=0 take x=cos(θ) 7x2+2x-7=0  x1, 2=-b±b2-4ac2a x1, 2=-2±22-4· 7-72· 7 x1, 2=-2±…

Q: The formula for cos(a- B) is sin a sin B- cos a cos B cos a cos B + sin a sin B cos a cos B - sin a…

A:

Q: Verify the identity by following the steps below. sin(x)cot(x) cos(x) 1) Write the left-hand side in…

A: To verify the identity sinxcotx=cosx.

Q: |Verify the following identities by converting the left side into the right side step-by-step. Write…

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Q: Write the following in terms of cos 0 only. sec 0

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Q: If an answer is undefined, enter DNE. sin (90°) = cos (90°) = %3D

A: To give the value of the following trigonometric ratios. sin90ocos90otan90ocot90osec90ocsc90o

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

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Q: Which of the following is not true? a) cos?t+ sin²t = 1

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Q: Which of the following is equivalent to sin 4? COS 4 b. COs C 17 tan C 15

A: Solution ) sin A = 15/17 cos A = 8/17 tan A = 15/8  cos C= 15/17 tan C = 8/15 Hence sin A = cos C

Q: If cos a = 0.565 and cos ß= 0.867 (both angles are acute),

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Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Given identity as 1+cos23θsin23θ=2csc23θ-1 Consider LHS : 1+cos23θsin23θ

Q: What is the formula for cos (A/2)

A: We have to find a formula for cosA2

Q: 10. Complete the following equation. sin (a-B)=sin a cos ß cos asin ß sin (a-B)=sin a cos B (1)-…

A:

Q: Use an addition or subtraction formula to find the exact value of…

A: Given:

Q: If sin A =0 1/3 with 90° &lt;=A &lt;=180° and sin B = 3/5 with 0° &lt;= B &lt;=90°, find each of the…

A: Given: sin A = 13 with 900 ≤ A ≤ 1800 and sin B = 35 with 00 ≤ B ≤ 900   To find:            cos A2

Q: Solve the following equation for 0<x < 2T. You credit. Answers must be exact. Cos x = V3 cos x…

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Q: Evaluate the expression without using a calculator. cos T 6 6 sin TT

A: From unit circle cos(pi/6)= sqrt(3)/2 sin(pi/6)=1/2

Q: The term cos(2a) can also be written as ... O 2 cos? a – 1 2 sin a – 1 O2 sin a cos a sin? a + cos?a

A: Let, cos2α=cosα+α Since, cosA+B=cosAcosB-sinAsinB

Q: (a) 10 cos 100t + 3

A:

Q: Verify the identity by following the steps below. sin(z)cot(r) cos(z) 1) Write the left-hand side in…

A: Given: sin(x) cot(x)= cos (x)

Q: Verify the following identities by transforming one side of the equation to the other. (a) cos θ(tan…

A:

Q: 12. Determine the correct simplification of the expression tan acos a+ cos a. a. sin? a b. cos a sin…

A: Given: tan2α cos2α+ cos2α

Q: What is the value of cos 6. а. 1 b. 2 V3 C. d.

A: Given that: cosπ6

Q: What is the exact value of cos(495°)? A 3 2 2 D 2 2. wish B

A: All trigonometry ratios change at 90° and 270°. In second quadrant , sine and cosine are positive.

Q: Find the value of the following cos-1 ( 3 + j )

A: The formula for is calculated as follows.

Q: Simplify: cos^4 A − sin^4 A

A: In this question, we need to simplify cos4 A -sin4 A.

Q: which of the following is equal to 1? a. tan20 + sec²0 b. -cot?e + csc²e c. sin?O tan²O d. sin?0 –…

A: Answer: b.-cot2θ+ csc2θ

Q: 2-Simplify first, then determine the exact value. (sin7n/24 + cos7a/24)2

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Q: sin(2t) cos(3¤

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Q: If sint = 4/5 and t is in the first quadrant, find cos(2 t) -7/25 -9/25 7/25 24/25 None of these

A: There is more than 1 question, as per the Q&amp;A guidelines I am answering the 1st question. If you…

Q: COS Coso xdxx

A: ∫cos6x dxApplying reduction formula with n=6 := cos5x sinx6 + 56∫cos4x dxApplying reduction formula…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.