In Exercises 43–44, express each product as a sum or difference. 43. sin 6x sin 4x 44. sin 7x cos 3x

Q: 29. Show that sin x rif0<1 <2m.

A: Given a function sin x and 0&lt;x&lt;2π To show sin x&lt;x for all values of x such that…

Q: Express the product as a sum or difference. 1. sin 4x sin 8x 2. sin 7x cos 5x

A: For the expression sin 4x sin 8x, multiply and divide the expression by two.

Q: The expression sin(3z) cos (2z)- cos (3) sin (2z) is equal to cos (5z) sin z cos z O sin (5z)

A: Trigonometry Addition Formulas The following are the trigonometric addition identity formulas for…

Q: Verify the identity. (7 cos x-4 sin x)2 + (4 cosx+7 sin x)2 = 65

A: Given,           7cosx-4sinx2+4cosx+7sinx2=65

Q: Write the expression sec(0) tan(0) in terms of cos(0) and sin(0). 1 cos(0) O sin(0) cos (0) O sin(0)…

A: We have to write the given expression in terms of cos and sin.

Q: From the list below find the expression, identical to the given. tan 4x sin 8x + sin 3x cos 3x + cos…

A:

Q: In Exercises 45–46, express each sum or difference as a product. If possible, find this product's…

A: 45. sin2x - sin4x

Q: Suppose that sin(θ)=4/8. What tan(θ)=______.

A:

Q: 1. Explain why sin(n+0) =-sin@ using a diagram and x, y, and r.

A: Solution of given problem is followed by

Q: 16. Verify sin(180° – ) = sin e (SHOW WORK)

A: We know that sin(a-b)=sina cosb-cosa sinb

Q: Verify that the equation is an identity. (Hint: sin 2x = sin (x+ x)) sin 2x = 2 sin x cos x…

A: Given identity issin 2x = 2 sinx cos x prove it?

Q: tan 6= .and 0s@s90 , then sin 0- O V3 2. V5

A: Solve for sin theta

Q: Be sure that you've familiarized yourself with the second set of formulas presented in this section…

A: Solution:We have to solve first three question9. sin 6x+sin2x10. sin8x+sin2x11.sin 7x-sin…

Q: 1. The formula sinusinv 5(cos (u - v) - cos (u + v)] converts a product of sines to a of

A: sinusinv=12cosu-v-cosu+v

Q: Express as a product.sin cos θ + sin 2 θ

A: To express sinθ cosθ+sin2θ. Solution: We know that, sin2θ=2sinθ cosθ Therefore, given expression can…

Q: 57 tan 4 177 Determine the value of x if D, sin(7-x)= csc 3 6. where 0sxST.

A:

Q: Be sure that you've familiarized yourself with the first set of formulas presented in this section…

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: Determine the value of 0 in sin(40 + 2°)csc(30+5°) = 1 O 3° O 4° O 5° O 2°

A: sin(4θ+2°)csc(3θ+5°)=1sin(4θ+2°)×1sin(3θ+5°)=1

Q: Prove the identity. sin x + sin 3x cos x + cos 3x tan 2x Use the Sum-to-Product Formulas and then…

A:

Q: Verify the identity: 4 cos x cos 2x sin 3x = sin 2x + sin 4x + sin 6x

A: We have to verify the identity: 4cosxcos2xcos3x=sin2x+sin4x+sin6x We know that…

Q: Express as a product.sin 3t - sin 7t

A: Given : sin 3t - sin 7t

Q: Prove That 4 Sin ³²A - CoS 3 A +4 Cas³ A - Sin 3 A = 3 Siny A

A: We need to prove: 4sin3A.cos3A+4cos3A.sin3A=3sin4A

Q: True or False sin ( 20) has two equivalent forms: 2 sin 0 cos 0 and sin² 0 – cos 0

A: Given statement is, sin2θ has two equivalent forms: 2sinθcosθ and sin2θ-cos2θ.   The objective is to…

Q: For Exercise 68, Section 5.2, exercise 68: sin^4 α - cos^4 α / sin ^2 α - cos^2 α=1

A: exercise 68: sin^4 α - cos^4 α / sin ^2 α - cos^2 α=1

Q: Part 3 of 4 COS X d —CSC X + С dx To check for the result, prove that 1 - cos?x

A:

Q: (45°) – tan (45°). Give the exact value of sec 2, 1 2/3-3

A: Use the trigonometric table to solve the given problem.

Q: Prove 3n - T, 2 sin? x – sinx cosx – 2 cos? x=0 in has five root's Hint. Intermediate value theorem

A: Corollary of Intermediate value theorem :- If a continuous function has values of opposite sign…

Q: Find the exact value of the expressic ܪܕܐ -1 sin sin ၁ 5 သ | O 2n O 2n 5 5 Эт O 3n 5 3 5

A:

Q: Expand sin(50) in powers of sin(0) and cos(0).

A: In this question we have to expand sin5θ in powers of sinθ and cosθ. we know,…

Q: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: Express the product as a sum or difference. 1. cos 3x cos 2x 2. sin 5x sin 8x

A:

Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: 7. tan (8x) sec (8r) da

A:

Q: Show that sin , +sin ¤, = 2 cos[;(4, – Þ,)]sin[;(P, +Ð,)]

A:

Q: 5) prove that = sin 'x +e using method of trigonometric substitution.

A: To Prove- Prove that ∫dx1 - x2 = sin-1x + c using method of trigonometric substitution.

Q: Express the sum or difference as a product. 1. cos 9x/2 + cos 7x/2 2. sin 4x - sin 6x

A: 1) Use the identity for summation,

Q: What mathematical result is applied to prove that sin^2(e)+cos^2(0)=1?

A:

Q: Prove that ²-1 (²) (0) (sin (+,-) + do r² sin(0)

A: Given : ∇2=∂2∂x2+∂2∂y2+∂2∂z2 To Prove : ∇2=1r2∂∂rr2∂∂r+1r2sinθ∂∂θsinθ∂∂θ+1r2 sin2θ∂2∂ϕ2

Q: Express as a product:Sin 8u + Sin 2u

A: Given sin 8u+sin 2u. we need to express the given term as product.

Q: 2) Explain why sin(8) = cos(90-e). %3D

A:

Q: verify the identity  1 + sec ^2 x/ 1 + tan ^2 x = 1+ cos^2x

A: Note that 1+tan^2x = sec^2x  1/sec2x= cos2x

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. csc(x) = 8, tan(x) < 0 %3D sin(2x)…

A:

Q: Prove that sin 4A = 4sinA cos³A – 4 cosA sin'A.

A: we have to show that the following

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

A:

Q: 1. Verify the expression cos(x) + sin x tan x = secx.

A: Given, cos x + sin x tan x = sec x

Q: Prove using trig identities sin 20° =1 V3 cos 20° – 2 sin 40°

A:

Q: Express as a product.sin 8t + sin 2t

A: We have to express the given trigonometric expression in product form: sin 8t+sin 2t We know the sum…

Q: tan 45, sec 60 5 sin 90 sin 60° 2 cos 0 cos135° Leave your answer in exact form (no decimals). 11.…

A: We will directly out the values of all of these then calculate.

Q: To evaluate sin 2x cos 2x dx , the identities to be used is/are: sin4x , 1+ cos4x A 2 2 ® cos?2x=1-…

A: To find The identities to be used.