prove that tan^2 (x/2)=1-cosx/1+cosx

Answer 1

let A = x/2 , then we are proving
tan^2 A = (1-cos(2A))/(1 + cos(2A))

LS = sin^2 A / cos^2 A

RS = (1 - (cos^2 A - sin^2 A) )/(1 + cos^2 A - sin^2 A)
= (1-cos^2 A + sin^2 A) / (1-sin^2 A + cos^2 A)
= (sin^2 A + sin^2 A)/(cos^2 A + cos^2 A)
= 2sin^2 A / (2cos^2 A)
= sin^2 A/cos^2 A
= LS