Question

Verify: sin^2x/[2-2cosx] = cos^2(x/2)

Answer 1

use the identity
cos x = 1 - 2 sin^2 (x/2)
substituting

sin^2 x / (2 - 2 cos x) = sin^2x / [2 - 2(1 - 2 sin^2 (x/2)]

= sin^2 x / 4 sin^2 (x/2) ...........................(1)

Now use the identity

sin x = 2 sin (x/2) cos (x/2) giving:-

sin^2 x = 4 sin^2 (x /2) cos^2 (x/2)

and substituting for sin^x in (1) and you have it.
2

Answer 2

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