ConceptTrigonometric Identities

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#### Question

Prove that sin^{6}θ + cos^{6}θ = 1 – 3 sin^{2}θ. cos^{2}θ.

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#### Similar questions

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 } )`

Choose the correct option. Justify your choice.

9 sec^{2} A − 9 tan^{2} A =

(A) 1

(B) 9

(C) 8

(D) 0

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

If sinθ + sin^{2} θ = 1, prove that cos^{2} θ + cos^{4} θ = 1

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)`