1.

Prove that sin6θ + cos6e+ 3sin2θcos26-1.

Answer»

sin^6 x + cos^6 x

= (sin^2 x + cos^2 x) ( sin^4 x - sin^2 cos^2 x + cos^4 x)

= (sin^4 x + cos^4 x) - sin^2 x cos^2 x

= (sin^2 x + cos^2 x)^2 - 2 sin^2 cos^2 x - sin^2 x cos^2 x

= 1 - 3 sin^2 x cos^2 x


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