TT 31. cos X TT sin x 32. cos x + -sin x TT 33. sin(x + п = cos X 34. sin( x - = -cos x 35. cos (A different derivation.) B) = cos A cos B + sin A sin B (Exercise 57 provides a 36. sin (A – B) = sin A cos B – cos A sin B

Q: 2. One of (a)-(c) is incorrect. Find and correct the mistake. (a) - sin(y³) = 2y cos(y?) (b) dx…

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Q: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2) and sin y=1/4 and y is in the interval (…

Q: (23) If f(x) = sin zx, find the value of fe (x). 23 sinx %3D 23 e. sin x a. 23 b. cosx . 1 cos TEX…

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Q: = 0 If 2 sin x cos x + V2 cos x = 0. 0, then %3D %3D or

A: 2sin x cos x +2cos x=0

Q: sin (+) can be expanded to: π TT O sin COS sin sin 4 7 TT O sin sin COS cos 4 T Osin COS + cos sin…

A: Solved below.

Q: 4 Se + 5x* + 10 cos x + 2)dx 5e" + x° + 10 sin x + 2x + c 5et + x 10 sin x + 2+c - et x° + cos x + 2…

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Q: 3. * S cos(3z)sin1º(3z) dz A 1 C (sin(3z))10 + C 3 (cos (3z))10 + C - -- В 1 (cos (3z))'1 + C 33 1…

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Q: If e /2i =sin2 then z = /21 - 2 In(sin2) + 4kTt – 2i In(sin2) – 4kt | 2i In(sin2) + 4k T - 2i…

A: We use the identity e^(2πki)=1 and by tanking ln both sides and then calculate.

Q: If x = 3 sin(0), then а. V9 + x? cos(8) 3 b. cos(x) Vx2 + 9 C. tan(x) d. cot(x) = 3 || е. sec(x) 3 O…

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Q: sin 2x, Which of the following is equal to sin x cOs x + C 2 sin x + C Option 1 Option 2 sin 2x + C…

A: As we know that the trigonometric identity: sin2x=2sinxcosx And ∫a·fxdx=a∫fxdx Given: I=∫sin2xsinxdx

Q: e 12 Cos V7t + sin 5 -- choices: sin V5 12s-7 s2+7 4. 12s-7 V5 s2+5 B s2+7 4. sin /5 12s-7 s2+7 36…

A: Solution

Q: Find , where : = sin (x²) cos (y) COS 6.x sin (a) cos (y) 2.x sin (a) O2.x cos (2) 2r sin (2*) cos…

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Q: Q4:B/Simplify [cos 20-i sin2018 [cos 30+ i sin30 1² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De…

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Q: 1. The expression sin(x +y) +sin(x-y) is equal to A. 2 sinx siny B. 2 sinx cosy C. 2 cosx siny D.…

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Q: (1+sinx)9 cos x dx , u=1+sinx is The values of a. (1+sinx) 10 + C 10 b. (1+sinx)10+ c 1 (sinx)10+c…

A: Solution: The objective is to find the value of the given integral

Q: 15 and x terminates in guadrant III. 17 Find sin2x, cos 2x, and tan 2x if sin x= - sin 2x cos 2x %3D…

A: The solution is given in the next step.

Q: Using an appropriate substitution, f sin³ (x)cos®(x)dx is equal to: sinx + C sin13x + C 13 sin11x…

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Q: – 1) sin a cos a - sin æ 9(cos² e – 1) O 9 tanx + 9 sec a O 9 cot a + 9 cscx O 9 tana + 9 csc a O 9…

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Q: 8 and x terminates in guadrant III. 15 Find sin 2x, cos 2x, and tan 2x if tanx= sin 2x %3D cos 2x…

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Q: What is the general solution of (sin 0 – = 0 ? 2rcos? 0) dr + rcose (2rsind + 1) do O sin 0 rcos e =…

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Q: s³(Ø) + sin(20) – 3 cos(0) cos F(8) de = J sin (ø) + 3 cos²(0) + 2 sin(8) – 3 Hint: Try substituting…

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Q: 9. cos (21) di 10. 11. sin'x cos's de 12.

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Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: Compute / sin? æ dæ. sin 2x + C 4 sin a +C 3 cos 2x + C 4 2 sin 2x + C 4 cos 2x + C 4 2

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Q: Find if r = sin[cos(-0)]. de dr = sin 0 cos(cos 0) de dr cos[sin(-0)] de Option 3 Option 1 dr dr sin…

A: This question is based on application of Derivative.

Q: Given that sin“ x + cos²x = 1 V2 and sin x = 5 what is the possible value of cos x

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Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: In Problems 28–44, establish each identity.

A: Trigonometric identities are given, we have to prove the identities. Note: we are answered with 3…

Q: 85. z = Cos xy -y² cos xy -y sin xy, Əx %3D %3D = -yx cos xy sin xy - дудх 22- = - SII ty, x-cos xy…

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Q: Find the exact values of sin and cos for sin e= on the interval 0° s es 90°. 2 sin 0.1691, cos…

A: We know that,  cosθ=1-sin2θ         cosθ>0 in 0°≤θ≤90°        ⋯⋯1sinθ2=1-cosθ2…

Q: 3. у"-2у'— sin 4x 1 cos 4x 40 1 sin 4x 20 Ans. y= c, + c,e²* + -

A: To find: The general solution of differential equation. Given: The differential equation is…

Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin301² [cos 40+ i sin40 1³[cos 20-i sin2015 using De…

A: The given expression,      cos 2θ-isin 2θ8cos 3θ+isin 3θ2cos 4θ+isin 4θ3cos 2θ-isin 2θ5 De Moivre's…

Q: 12. Given that V3 cos x = cos(-x), tan x= A 3. cos(f B V3 C 1. V3

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Q: 2 tan 4x dx The is equal to 1- tan 24x A. In(sec 8x) + C B. In(sec 8x)8 + C 1 C. In(sec 8x) + C D.…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 12. Which is not a solution to the equation sin x = cos x-1? %3D A. x = 1 B. x == C. x = 3n 13.…

A: We will find the correct options for each question as following.

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: 1) Using the formula: cos(x +y) = cos x cos y – sin x sin y, prove in steps that: cos? x = 1+cos 2 x

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Q: Q4:B/Simplify [cos 20-i sin20][cos 30+ i sin3012 [cos 40+ i sin40]³[cos 20-i sin2015 using De…

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Q: 21. y = csc 2x 22. y = tan 2 Vx* + 1 x tan x 24. y 23. у x? + 1 1 + sin? x

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Q: Graph the functions in Exercises 13–20. What is the period of each function?

A: Dear student, Since you have posted multiple questions, as per our policy we will answer first…

Q: Which is equal to (sin⁡x+cos⁡x)^2+(sin⁡x−cos⁡x)^2 using identities?   −2   1   2   −1

A: We have to find

Q: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2).sin y = 1/2 and y is in the interval (π/2,…

Q: Solve the equa tion on the interval [ o, 2 ) 2 sin? 9-3 sin O +1 =0 tan2x-1 =0 (2 cos x +JE) (2 sin…

A: As per bartleby guidelines we only give first three question answers.

Q: sec 0 + In + 27+3 = -3 2 In y? + 327 – 4 = 1+ cos 20 2/1+ (tan 0)² + 2ln /y + 22 = -3

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Q: 23, sin 50° + sin 40° 23. sin A VZ cos 5° B 2 cos 10° 2 cos 5° D V2 cos 10°

A: Trigonometric identity: sin x+sin y=2sinx+y2cosx-y2

Q: 1. If x-y? = 25, then y" = %3D a.) b.) c.) - d.) - 2. If y = cos(3x+1), find y' a.) 3 sin(3x+1) b.)…

A: Given:   (1) x2 - y2 = 25    (2) y = cos(3x+1)

Q: sin 5x sin adx =? O A, sin 4x sin 6x +c 6 4 sin 4x sin 6x OB. 8. +c 12 O C cos 4x 8 cos 6z +c 12 O D…

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Q: de 2- sin(e) ( cos(e) de 1+cos(0) de 2- 3sin(e) de 3sin(e) + 4cos(e) + 5 de sin(e) + 3cos(6) + 3

A: SOLUTION Given ∫dθ2 -sinθ∫cosθ dθ1+cosθ∫dθ2-3sinθ∫d θ3 sinθ+4 cosθ+5∫d θsinθ +3 cosθ+3 we need to…

Q: 12 and x terminates in guadrant I. 13 Find sin 2x, cos 2x, and tan 2x if sinx= sin 2x %D cos 2x %3D…

A: Given: sin x=1213and x terminates in quadrant I. To find sin2x, cos2x, tan2x The hypotenuse side is…

Q: Find LT of (i) e-*(2 cos 5t – 3 sin 5t) (ii) e²ª cos² t (iii) e“ sin 2t cos t ,4t

A: