Prove that (1+sinx-cosx/1+sinx+cosx)^2= 1-cosx/1+cosx

Answer 1

For ease of reading, I'll just use s for sinx and c for cosx

(1+s-c)/(1+s+c)
= (1+s-c)^2/[(1+s)^2-c^2)
= (1+s-c-sc)/(s+s^2)
= (1-c)(1+s)/(s(1+s))
= (1-c)/s

That means that

[(1+s-c)/(1+s+c)]^2 = (1-c)^2/s^2
= (1-c)(1-c) / (1+c)(1-c)
= (1-c)/(1+c)