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, where the angles involved are acute angles for which the expressions are defined.

`(1+ secA)/sec A = (sin^2A)/(1-cosA)`

[Hint : Simplify LHS and RHS separately]

Prove that `\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }+\frac{\sin\theta +\cos \theta }{\sin \theta -\cos \theta }=\frac{2}{2\sin^{2}\theta -1}`

Prove that: `(1 – sinθ + cosθ)^2 = 2(1 + cosθ)(1 – sinθ)`

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