Prove that 3 12 56 -1 -+ cos 5 sin sin 13 65

Q: cos 30° + sin 60° V3 Prove that 1+ cos 60° + sin 30° 2.

A: Given to prove : cos30∘+sin60∘1+cos60∘+sin30∘=32…

Q: Prove: sin (2 cos x)= 2x1-x² %3D

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Q: 11. Prove the identity. sin 6.4 = 3 sin 2.4 – 4sin 24 12. Prove the identity. cos30 = 4cos 0- 3cose

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Q: Prove the identity:  4 sin (3x) cos (4x) = 2 sin (7x) - 2 sin (x)

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Q: B- If x+= = 2 cos Ø prove that x"+ 2 cos rø by used complex number.

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Q: using De-Moivre's theorem prove that cos π/7, cos 3π/7 and cos 5π/7 are the roots of 8x3-4x2-4x+1=0.…

A: The given equation 8x3-4x2-4x+1=0 Roots of the equation are cosπ7, cos3π7, cos5π7 use trigonometric…

Q: 2 2 In sin 2x - 2 In (1 + cos 2x) = In ( )- %3D

A: Given that: The identity is 2 ln sin 2x - 2 ln ( 1 + cos 2x) = 2 ln tan x .

Q: Let z1 = 4 (cos 7π/12+ i sin 7π/12) and z2 = 2 (cos 5π/12+ i sin 5π/12) Find z1z2. Find z1/z2

A: Recall:  z1z2=r1r2cos(A+B)+isin(A+B) z1z2=r1r2cos(A-B)+isin(A-B) We have, r1=4, r2=2, A=7π12,…

Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: 5. Evaluate π/3 π/6 cos3 x sin−2 xdx.

A: 5.Solution…

Q: 14. Prove that (1- cos x) csc x = 1

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Q: 8. Express the product sin30 cos50 as a sum. 1/2 (sin80-sin20) 1/2 (sin80+sin20) sin80-sin20…

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Q: 1 Evaluate sin (7/6 + 2e de. 2ei de. 2n Jo

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Q: Prove the following: 1+2sin cos sino + cose = sin 0+ cos 0

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Q: Prove cos 4x = 8 cos4x − 8 cos2x + 1.

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Q: 1 Prove that sec 03D Cos 0

A: Let P(x,y) be a point on a circle of radius r associated with the angle θ.

Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de =- (1-cos a). CO TE/2-a

A: We will use the Differentiation under Integral sign method, to solve the problem.

Q: B- If x+ 2 cos0 prove that x" +2 cosro by used complex number.

A: we have to show that the following

Q: prove cos^4x-sin^4x=xos2x

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

Q: Prove that (7 sin2m-10 cos2n-10 = – B(m,n)

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 7π/12+

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Q: 10. Prove that 7/2 sin 0 cos (cos a cosec 0) do -(1-cos a). 2 ||

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Q: Prove that X +. 8 2 1 sin x X sin 8 2 sin %3D

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Q: 1 1 Prove 2 csc? x 1- cosx 1+cos.x

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Q: 1. Prove the following identity (4) cos(2x)cot(2x)=2-cos(x)(2x)+sin(x)(2x)

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Q: Prove the following identity 1+ cos(2x) 1 sin(2x) tan(x) 1+ cos(2x) sin(2æ)

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Q: B- If x+! += 2 cos prove that x"+= 2 cos rø by used complex number.

A: we have to show that the following

Q: prove that: a- cos20 = cos²0 – sin²0 %3D sin20 = 2sin0cos

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Q: prove that sin(45° + A) sin(45° - A) = 1/2cos2A

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Q: Prove that cos 17° + sin17° tan62° %3D cos17° – sin17°

A: Devide the whole left side by Cos17° and use formula of tan(a+b)

Q: 4. Prove that equations are identities. l– cos4x a) tan 2x =, 1+ cos 4x

A: Given:

Q: 10. Prove that 7/2 TC/2- sin 0 cos (cos a cosec 8) de -0 2 (1-cos a).

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Q: Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

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Q: Use the addition formula to prove                                                             cos 3θ…

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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: 13л +i sin 16 5л +i sin 8. 13л 5л Let Z1 = 10| cos and Z, = 2| cos 16 8

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Q: do o find 4+ 3 sin 0

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Q: Prove : sin 3θ = 3 sin θ + 4 sin3 θ

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Q: 18. Prove tan (0)+1= sec (0) 19. Solve: 2cos? (3x) + 5cos (3x)- 3 = 0 a. b. 4 cos

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Q: 1-cos^3A/1-cosA = cos^2A + cosA+1

A: 1-cos3A1-cos A=cos2A+cos A+1

Q: Prove that 2cos^x_1=cos2x

A: In this question we have to prove 2cos2x-1=cos2x

Q: Prove cos 4x = 8 cos4 x - 8 cos2 x +1.

A: In trigonometric ratio,cos2θ=2cos2θ-1

Q: 17 prove 4 Cos" ☺ - Sin" 0 = Cos20

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Q: show that. 19 -18 O Sin 8= ē-e 2) Sin(-9) = -Sing 3) coshio = cose %3D 2.

A: Here we use the properties of trigonometric functions and hyperbolic function.

Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de re/2-a (1–cos a). 2

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Q: 8

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

Q: 24. (sin 0°)(tan 30°) + cos 0° 26. cos 60°(cos 0° - cos 180°) 25. (cos 180° + 2 tan 45°) 27. (sin…

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