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Solution - Trigonometric Identities

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Question

Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.

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Prove the following identities:

`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`

`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`

`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`

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Choose the correct option. Justify your choice.

9 sec2 A − 9 tan2 A =

(A) 1

(B) 9

(C) 8

(D) 0

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If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p2 – 1) = 2p

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If sinθ + sin2 θ = 1, prove that cos2 θ + cos4 θ = 1

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Prove the following identities:

`(i) 2 (sin^6 θ + cos^6 θ) –3(sin^4 θ + cos^4 θ) + 1 = 0`

`(ii) (sin^8 θ – cos^8 θ) = (sin^2 θ – cos^2 θ) (1 – 2sin^2 θ cos^2 θ)`

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