Prove the identity: sin(0)-co sin (0) +cos (0)–1 cos (8)+1 sin(0)+1 cos(8)

Q: 2. Prove the identity: (cos x- sin x)2 + (cos x + sin x)2 = 2. %3D

A: To prove  that cosx-sinx2+cosx+sinx2=2

Q: Express cos- (a) in terms of cos(2a). Express sin (a) in terms of cos(2a).

A: This question is of double angled identity.

Q: Verify the identity. 6 cos2(x) – 3 = 3 – 6 sin?(x) - (| ([ 6 cos?(x) – 3 = 6(1 3 - 3 = 6 – = 3 - 6…

A: Given: 6cos2x-3=3-6sin2x We have to verify the given identity. Formula used: sin2x+cos2x=1

Q: 10- Sin'x- cos'x is equal to: a)2x b)1 c)-1

A: 10-sin^2(x) -cos^2(x) We apply trigonometry rule

Q: Prove the identity. 3 sin(x - y) 3 tan x - 3 tan y = cos y cos x

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

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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: 2) VERIFY THE IDENTITY sin +0 =-cos 0. 2.

A: We need to verify the identity.

Q: Prove the identity. 3. cos X sim x= 2. S1in X-Sin x) COSX

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Q: Verify the identity : cos (x - π/4) = √2(cos x + sin x)/2.

A: We use cos(A-B)=cosAcosB+sinAsinB formula

Q: Complete the identity. (sin x + cos x) cos x)- 1+2 sin x cO X O A. 1- sin x O B. 0 OC. sec x O D. 1

A: use (a+b)2 = a2 + b2 + 2ab and sin2 x + cos2 x = 1

Q: 2 cos" (x)–sin°(z)+1 cos(x) 3 cos(x) 10. Verify the following identity, justifying each step.

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Q: Prove the identity cos(x+y)cos y +sin(x+ y)siny =cos x

A: We have to prove the identity                              cosx+ycosy+sinx+ysiny=cosx

Q: cos 2x +1 Prove that sin 2x

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Q: What is (cos x + x) dx? O-½ sin²x + x²/2 + C ○ -sin x + x²/2 + C O sin x + x²/2 + C O. ½ sin²x +…

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Q: Derive/Prove: sin 2x = 2sin xcos x Useful Formula: cos 2x = cos?x-sin? x a. = 2 cos x-1 =1-2sin x…

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Q: Prove the identity (sin x + cos x)? – sin(2x) =1

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

A: According to the difference of squares formula, (a+b)(a-b)=a2-b2. Using the difference of squares…

Q: (a) Prove that Sin-1x  + Cos-1 x  = π/2 .(b) Use part (a) to prove Formula 6.

A: a) We have to prove sin-1x+cos-1x=π2 Let sin-1x=θ                                     ⋯⋯1…

Q: Find 1+sin -cos I COS In | sin - z+cos In In 1+tan +C +C +C +C

A: We can evaluate the given integral by using the substitution u = tan (x/2).

Q: Verify the identity. 2 sin(x) cos(x) = 1 (sin(x) + cos(x))2 - 1

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Q: Verify the identity. cos(e) sin(0) - csc(0) 1- sin(0) cos(0) - cot(0) sin(e) – sin(0) sin(e) –…

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Q: the sum of sin h 2x and cos h 2x

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Q: Prove: sin? x 2 cos“ = cos 2-2cos x

A: We will use basic properties of trigonometric ratios

Q: cos 2r Verify the identity: = cos x + sin x. sin x cos X

A: Verify the following: cos 2xcos x-sin x=cos x+sin x

Q: 4. Prove the identity csc 0 – sin 0 = cot 0 cos 0.

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

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Q: Verify the identity. 6 cos(sin-1 x) = / 36 – 36x2 Let 0 = sin-1 x = sin 0 = x = X. Thus, 6 cos(sin-1…

A: use trigonometric identity  to verify it.

Q: 1+ sin 0 . Verify cos O 2 sec e Cos A 1+ sin A

A: Our Aim is to verify 1+sin θcos θ+cos θ1+sin θ=2 sec θ -(i)

Q: 2. Prove the identity: cos (x-y)– cos (x+y) = 2 sinx siny

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Q: 16. Establish the identity: os 0)² + (sin 0- cos 0)2 = 2 %3D

A: We need to establish the identity  (sinθ+cosθ)2+(sinθ-cosθ)2=2

Q: Verify the identity (1+sin x)(1-sin x)=cos2x   (sin x + cos x)2 + (sin x - cos x)2=2   cot(x) =…

A: (1+sin x)(1-sin x)=cos2x Apply FOIL method to expand left side

Q: - Prove that tan 0 + cos 0 sin 0 cos 0 cos 0T sin 0 - Prove that cos? 0 – sin² 0 cos? 0 + sin A cos…

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Q: (cos^4 x) - (sin^4 x) = cos2x   verify the identity

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Q: cos e sin 0 for some real value of 0, and let B= -1 Let A = Consider x - sin 0 cos 0 Then ||(AB)x||…

A: Given,            A=cosθsinθ-sinθcosθ , B=0-1-10 , x=12To find : ABx

Q: Cos (GX) = Cos 15°, 0°<x < 360° Со X) = Cos 15°, O° < x < 360° %3D Tan( x ) = tan,05x < 2n )= tan,

A: We can find the answers as below

Q: 3 Verify the identity: csc (0) 1-cos2 (0) cos (20) 2 sin(0) + 2tan(0) cos(0) = %3D sin (0)

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Q: Prove the identity. sin(n-x)сos(n+x)tan(2π − x) T 3π 3π sec+ x)csc(³7-x)cot (³7 + x) = sin^x - sin²x

A: I have appended the formula used in the solution part of the question

Q: sin 0 13. Prove that 1 - = Csc 0(1 + cos 0). Cos 0

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Q: sin 0(3sin? 0+ 4cos? 0) = 3 cos 0 + cos³ 0 4. Prove that tan 0

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Q: Verify the identity: [cos(x + h) - cos x]/h = cos x. (cos h - 1)/h - sin x. (sin h)/h

A: we have to verify the identity : cos(x+h)-cosxh=cosx(cosh-1)h-sinx(sinh)h

Q: Prove the identity. 3 sin(x – y) cos y cos x 3 tan x - 3 tan y

A: Given that  3tanx-3tany=3sin(x-y)cosycosx We need to verify the given identity.

Q: Verify the identity. sin 40 = 4 cos '0 sin 0 – 4 sin °0 cos 0

A: To prove that  sin4θ=4 cos3θ sinθ-4sin3θ cosθ

Q: Verify the identity. 1- sin x + COs X 1 + sin x + cos X COS X | sin x + 1

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Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: Prove the identities: (x sin 0 – y cos 0)² + (x cos 0 + y sin 0)² = x² + y²

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Q: Verify the identity. sin (e + n) = -sin e A) sin (e+x) = cos Osin e- cosa sin a = cos Osin e--0 =…

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Q: 1- cos 0 1+ cos 0 sin 0

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Q: 7. Prove the identity. – sin 3 TT -x= 0 2 sin +x 2

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