Question

sin^4 theta + cos^4 theta-2 sin^2theta

Answer 1

You need only the identity that cos^2(a) + sin^2(a) = 1, or cos^(a) = 1 - sin^2(a).

Working on the left side only :

sin^4(a) + cos^4(a) = [sin^2(a) + cos^2(a)][sin^2(a) - cos^2(a)] = 2sin^2(a) - 1

Using the identity in the first form, sin^2(a) - cos^2(a) = 2sin^2(a) - 1

Using the identity in the second form, sin^(a) - (1 - sin^2(a)) = 2sin^2(a) - 1

Simplifying the left side, 2sin^2(a) - 1 = 2sin^2(a) - 1.

Note:

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