Trig Equation Problem?

Question

Prove:

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

Thanks!!!  

Answer 1

Left hand side =

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

From the trigonometric identities sin^2x +cos^2x = 1

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

a^2-b^2 = (a+b)(a-b)

consider a = 1, b = cos^2x

= [((1-cosx)(1+cosx))/(1+cosx)(1+cosx)]+1

Cancel the common term(1+cosx)

= [(1-cosx)/(1+cosx)]+1

= 1-cosx+1+cosx/1+cosx

= 2/1+cosx

= Right hand side