I'm reviewing for my exams, and I was sure that I was comfortable with solving trigonometric identities, but now that I'm looking at ones on my review, I'm not so sure. Could someone please show me, step by step, how to answer one?

Question

[cos^2theta] / [1 +2sintheta -2sin^2theta]
is equal to
[1 +sintheta] / [1 +3sintheta]

Thanks in advance :)

Answer 1

I think you have a typo - see my 3 below

-[1-s^2] / [3s^2 -2s -1]
(not 2s^2-2s-1)

[(s-1)(s+1)] / [ (s-1) (3s+1) ]