Calculate (cos + isin Hint: DeMoivre's Theorem: (cos x +I sin x "- cos nx +i sin nx

Q: Prove that 1-x ', V 2 1+x cos'x = 2 sin 2cos 2 COS 1 -1

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Q: Solve the equation for the values of theta between [0,2pi) 2 cos^2 θ - cos θ - 1 = 0

A: Given Data: Equation:  2 cos2 θ - cos θ - 1 = 0 Interval: [0, 2π) Factorise the given equation.…

Q: Show that A" cos (ах ah + b) = | 2 sin cos a + bx +n (ah + T 2

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Q: fOo)=Sinx-41 Cos x 1X-1 cos X (x)

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Q: Verify identity (csc x - cot x)2 =(1 - cos x)/(1 + cos x).

A: The given identity is csc x-cot x2 =1-cos x1 + cos x

Q: Verify the identity: sin²x (1+ncot²x) + cos²x (1+tan²x) = sin²x(n+cot²x) + cos²x(n+tan²x)

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Q: 57 sin 6 (똥 + 미) =글(c8 )%3D (cos w - V3 sin w) -

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Q: sin* x – cos* x = 1 x – cos? x

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Q: Prove that sin 0 - COS 2 2 = 1 - sin 0.

A: L.H.S. =sinθ2-cosθ22R.H.S. =1-sinθ

Q: Prove that sin 0 COS 0 2 2 = 1 - sin 0.

A: 1. sin2θ+cos2θ=1 2. sin2θ=2sinθcosθ

Q: 1 + tan2x=sec2x partiendo de la identidad cos2x+sen2x=1

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Q: 1 + sin x Differentiate y = x + cos x

A: As we know that: The Quotient rule: fg'=f'·g+g'·fg2 The Power rule: ddxxn=nxn-1 Given:…

Q: Prove sin(x+y)cos(x-y) = sinx/secx + cosy/cscy

A: I hope this can help you.

Q: Prove that sin? 0 + cosª 0 = sin“ 0 + cos² 0.

A: Using fundamental identity of trigonometry.