sin e 1 cos 0 Multiply - by 1 + cos 0 1 - cos 0

Q: Establish each identity.

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Q: Establish each identity.

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Q: sin 0- cos 0+1 sin0+1 (c) sin 0+ cos 0-1 cos 0

A: Given: sinθ-cosθ+1sinθ+cosθ-1=sinθ+1cosθ

Q: 6 sin(x) + 2 cos(x) = 0

A: We are given trigonometric equation as

Q: (÷++) + co« (5 - ). cos 3 x ) is equivalent to O cos 2x cos x O sin x cos x

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Q: 2 cos2(0) - cos(O) - 1 = 0

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Q: Solve ( sin θ - 2r cos^2 θ) dr + r cos θ ( 2r sin θ + 1) dθ = 0 a. r sin^2 θ - r^2 cos^2 θ = c b.…

A: Given that sinθ-2rcos2θdr+rcosθ(2rsinθ+1)dθ = 0. The objective is to solve the given equation.

Q: sin 2x 10. Simplify 1-cos x (a) 2cot x (1+ cos x) (b) sin 2x (1 + cos x) (c) sin 2x (d) – 2 tan x (1…

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Q: 16. Scos cos 0 cos (sin 0) de

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Q: (ii) Prove the identity (2 - 2 cos 0)(sin 0 + sin 20 + sin 30) -(cos 40 - 1) sin 0 + sin 40 (cos 0 –…

A: Prove the Identity: 2-2cosθsinθ+sin2θ+sin3θ=-cos4θ-1sinθ+sin4θcosθ-1 NOTE: Since you have asked…

Q: (cos(7+) +;cos(37x) +.) -1<x<0 7) S(x)=. 2r Ans. 0<x<1 2 sin(7 x) -sin(27 x) +

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Q: a sin if cos 0 = and 0 < 0 < b cos e if sin 0 = and < 0 < T C Cos 0 if sin 0 - 흥 and <0< 2T d sin 0…

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Q: 4 cos x + 2 sin r = 2 COS

A: As we know, Sin2x + cos2 x = 1 Since the interval is not given so we have to find general solution

Q: 9. cos 0 =: 24 * and n < 0 < 2n 25 sec 0 = sin 0

A: Use trigonometric ratio to solve

Q: sin(1+ cos(0)) Find lim 1+ cos(0) Select one: О a. -1 O b. 1 Oc-2 O d. 2

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Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: +sin(n")n-1 n6.1+cos(n2)n®+2 4. 2 9) Et sin (n* cos(n)

A: We have to use limit comparision test for checking divergence

Q: 65. 3 sin x = cos x 67. cosx- sin²x = 1 69. 2 cosx- 3 sin x- 3 = 70. 2 sin?x - cos x - 1 = C

A: 67. cos2x - sin2x =1 1 - 2sin²x = 1 Cos2x =1 2x = cos-(1) 2x = 0, 2π , 4π ..... x = 0,π,2π  So…

Q: COS M + Sin n 2 secn COS n

A: we can solve by using trigonometric identities  Sin2x+cos2x=1

Q: 4. sin(4x) = (4 sin(x) cos(x))(2(cos(x))² – 1) %3D

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Q: 7/2 sin 0 cos (cos a cosec 0) d0 6/2- (1-cos a). -COS

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Q: ƒ cos(x³) x² dx. 1 ¹ cos4 + c 4 1 WIT 3 1 -| sin x³+ C 1 ·cosª + c 4 4 -3 sin x³+ C

A: Topic = Integration

Q: sin(1) dt Using an appropriate substitution, evaluate: [2+ cos(t)]* A +C 3[2+ cos(t)]3 3 B +C [2+…

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Q: 3 sin(0 + 27) = 1 sin 0 cos O O - sin 0 2 sin 0 O sin 0 cos 0

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Q: a) 2(sin x)? – 1 = 0 [0,27] b) 6(sin x)² + cos 2x + 1 = 0 [0,2n] c) (cos 2x)2 + cos 2x + 1 = 0 [- ,…

A: (a) ⇒2(sin(x))2-1=0⇒(2sin(x)-1)(2sin(x)+1)=0⇒sin(x)=12 OR sin(x)=-12⇒x=π4, 3π4 OR x=5π4, 7π4

Q: 20. е -3.1х cos 2.1x, e -3.1х sin 2.1x

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Q: evaluate the integral

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Q: Cos 8 + sin 0 sin 0 1 cos 0 cos 8 sin e

A: As value of cosθ and sinθ revolves around +1 to -1 , they take different values depending on the…

Q: 1+ cos(0) sin(0) sin(8) 1 + cos(0) = 2 csc(0)

A: Given: 1+cosθsinθ+sinθ1+cosθ=2cosecθ

Q: sin 40 Evaluate the integral : do 3 + cos 40 using the substitution u = 3+ cos 40. sin 40 do = 3+…

A: Solve by substitution method

Q: 39. cos (7 + x) 40. sin(27 - x) 41. sin 42. cos + x 2

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Q: e identity: cos 3x = 4 cos x-3 X So

A: # we are entitled to solve one question at a time please resubmit the other question if you wish to…

Q: 1- cos e sin 0 sin 0 1- cos 0 23.

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Q: sin ²e + cos²e =(1)". if n>1

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Q: sin(cos (0.5354)) = O 0.8446 O 1.8446 O -0.1554 O -1.1554 O 2.8446

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Q: Cos 9 2 Sin e cos8 © cos (e) cos o (d) cos'x + 2 Sinx + 2 = o

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Q: Ísin^2 (x) cos^2 (x) dx * O 1/8 x -1/32 sin4x + C O 1/8 x - 1/32 sinx + C O 1/8 -1/32 sinx + C O…

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Q: 3 cos(0) sin(0) + 2 cos(0) = 0

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Q: π/2 0 sin³ cos Ode 0

A: This question is based on substitution method.

Q: 5 sin 0 – 4 cos 0 e of 5 sin 0 + 4 cos 0 is

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Q: 1+ sin 0 b) coso coso 1- sin 0

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Q: 8(x)=cos x,[0,2=]

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Q: 2 cos 2 ( x ) − 7 cos ( x ) + 5 = 0

A: Topic - trigonometric Equations Put cos 2x = 2 cos2 X-1

Q: 1 cos Cos (n + 1)² n n=1

A: A telescoping series is any series where nearly every term cancels with a preceeding or following…

Q: 8]. r = sin 0 -2 cos 0

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Q: Sin 4 Cos 4n %3D Sinn (osn

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Q: ∫ sin^3 2θ (√cos 2θ ) dθ

A: Integrate∫sin32θcos2θdθ  ..........1

Q: 2 + cos 0 = 1 + 2 sin² 0

A: The given equation is  2+cosθ=1+2sin2θ The given set of possible answers is  -π3,-π4,π6,π4,2π3,π,3π2…

Q: 1+ Cos 0 1-Cos 0

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