Be sure that you've familiarized yourself with the second set of formulas presented in this section by working 5–8 in the Concept and Vocabulary Check. In Exercises 9-22, express each sum or difference as a product. If possible, find this product's exact value. 9. sin 6x + sin 2r 10. sin &x + sin 2x 11. sin 7x - sin 3x 12. sin 11x – sin 5x 13. cos 4x + cos 2r 14. cos 9x - cos 7x 15. sin x + sin 2r 16. sin x – sin 2x 3x 17. cos+ cos 2 3x + sin 2 n 18. sin- 19. sin 75° + sin 15° 20. cos 75° - cos 15° 21. sin 12 5p sin 12 p 22. cos: 12 5p Cos 12

Q: #32

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Q: 2. Expand using a double angle formula. a) tan 5x b) -10cos 40x

A: Solving the problem with the using of double angle formulas.

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

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Q: Verify the given sum-to-product formula cos * + cos * = 2cos [(* + *)/2] cos * - */2}. Start with…

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Q: In Exercises 17-26, use an addition or subtraction formula to find the exact value. 17. sin- 12 18.…

A: Given 1)sin(7π12) 2) cos(105)We need to find the value using addition or subtraction formula

Q: a) Find the square root 14+ 4√6. b) If ƒ(r) = (2+1), show that ƒ(r) — ƒ(r+1) = r(r+1}(r+2). Hence,…

A: B. f(r) - f(r+1)

Q: 71. a. Is it true that sin (2 · 30°) = 2 sin 30°? b. Expand sin(2 · 30°) as sin(30° + 30°) using the…

A: To find sin(2 .30°)=2 sin 30°and Expand sin (30°+30°) using sum formula for sineFormula:sin 2θ =2…

Q: Evaluate (4 sin² x cos² x dx sin 2x cos 2x A) 1/2 In/cos2x| + C O B) -1/2 In/cos2x| + C O C) NONE OF…

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Q: Verify the identity. cos 3x + cos x = 4 cos3 x - 2 cos x Working with the left-hand side, use a…

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Q: Prove that the following identity is true. sin x tan x sin x cos x sin x - COs X cos x 2 cos x We…

A: The given identity is

Q: Evaluate sin 0 within AABC. A 25 24 7 sin 0 = Enter your next step here

A: A triangle is a polygon with three sides. A right triangle is a triangle with one of its angles…

Q: A 10-point question on a quiz asks students to verify the identity sin x – cos x sin x - cos x. sin…

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Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

Q: Final exact and simplified numerical values which applied to Fundamental Theorem F(b) and F(a) must…

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Q: 5. Show that de (tan 8) can be expressed in the form 3tan 8+3sec2e-3. Hence, find tan*e de.

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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: (a) Is it true that sin (2.60°) =2 sin 60°? Give exact answers in simplest form. (b) Expand sin…

A: We will use the following: sin(90+θ) = cos(θ) Sum formula for sine- sin(A+B) = sin A cosB + cos A…

Q: 11. Prove the identity. sin 64 = 3 sin 2A – 4sin³ 2.4

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Q: Evaluate sin 0 within AABC. 7 B 25 24 A sin 0 Enter your next step here

A: A triangle is a polygon with three sides. A right triangle is a triangle with one of its angle being…

Q: 3. Evaluate 5 sin rdr

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

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Q: Use de Moivre's theorem to show that sin 30 = 3 sin 0 – 4 sin 0. Hence solve 24x – 32x3 = 1.

A: De moivre's theorem states that (cos θ+isinθ)n=cosnθ+isinnθ

Q: Give a general formula for all the solutions. 7 sin 0+5=2 sin 0

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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: Write the expression as one involving only sin 0 and cos 0. sin 20 - cos 0 Choose the correct answer…

A: Given sin2θ-cosθ

Q: Show that cos bx = (eibx +e-ibx) and 1 sin bx :(eibx – e-ibx). 2i

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Q: Express the given product as a sum or difference containing only sines or cosines. sin (9x) cos (4x)…

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Q: Using the result of the previous question, explain why 1 n sin" xdx = - sin"-2 xdx. n and hence show…

A: The given problem is to show the result of given integral with using the given integral result.

Q: sin[sin^(-1)(3)/(5)+cos^(-1)(-(4)/(5))] =

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

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Q: Find an equivalent expression to sin (z+) a) sin(2)-√3 cos(z) 2 b) √3 cos(z)+sin(z) 2 O c) -…

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Q: Write the ratios for sin X and cos X. 12 5n Y 119 119 ,cos X = V119 a. sin X = sin X = %3D .cos X =…

A: XYZ is a right angle. So,                    sinX=ZYXY, and  cosX=ZXXY⇒sinX=11912, and  cosX=512

Q: 4. Express the given product as a sum containing only sines or cosines 170 30 sin cos |

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Q: tan 2.r As x gets closer to zero, what does get closer to ? In(1 + x)

A: Using L hospital rule

Q: Find sin(x/2), cos(x/2), and tan(x/2) from the given information. sin(x)=4/5 , 0˚< x < 90˚

A: Given,         sinx=45 , 0°&lt;x&lt;90° .

Q: Express sinh (i) in the form a + ib

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Q: Simplify the expression cos^2⁡x/1−cos^2⁡x A sin^2⁡x B cot^2⁡x C cos^2⁡x D tan^2⁡x

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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: ㅠ ㅠ Solve the problem. Usesin = = landsin = 4 ㅠ Use the formula sin(2x) = 2 sin x cos x, with x = 4…

A: We can find the answer as below.

Q: Write the product as a sum: 4 sin(14x)cos(5x)

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Q: sin 80 do Evaluate the integral 7+ cos 80 using the substitution u = 7+ cos 80. sin 80 do 7+ cos 80…

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Q: (I. If x = 2(1+ sin 0) and y = 3(0 – cos 0) find expressions for and in terms of sin 0 and cos 0,…

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: Find the exact value of sin 7π/12 using the fact that 7π/12 = π/3 + π/4.

A: Given:sin7π12

Q: Let sin A = 3/5 with A   sin 2 A

A: Given:sin A=35Formula:sin 2A=2 sinA cosAsin2A=1-cos2A

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

A: Given : sinx + sin 3xcosx + cos3x = tan2x

Q: Prove the identity. 9 sin(x- y) cos(x) cos(y) 9 tan(x) – 9 tan(y) Use a Reciprocal Identity, and…

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Q: Show all work and solve for all solutions of sin 0 cos 0 + 3 cos 0 = 0

A: To solve and find all the solutions of this trigonometric equation.

Q: 8

A: To rewrite the below expression using sum to product formulas