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I'm asked to verify this identity. I've been going at it for a hour now with no successful results. 
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2 Answers

If you want to prove from the left to the right, here is one way:
= (1-sin^2x + 1+sinx)/(1-sin^2x+3)
= (1+sinx)(1-sinx+1)/[(2+sinx)(2-sinx)]
= (1+sinx)/(2+sinx), after canceling 2-sinx.