Question

How would I go about proving this is an identity? Thank you. (1-sin^2(x/2))/(1+sin^2(x/2))=(1+cosx)/(3-cosx)

Answer 1

`LHS=(1-sin^2(x/2))/(1+sin^2(x/2)`

`=(cos^2(x/2))/(1+1-cos^2(x/2))`

`=(2cos^2(x/2))/(2-2cos^2(x/2))`

`=(1+cosx)/(4-(1+cosx))=(1+cosx)/(3-cosx)=RHS`