prove this identitiy Prove this identity 21 cosX tan2 X2

prove this identitiy

Prove this identity 2/1 + cosX - tan^2 X/2 = 1

Solution

2/(1+cosx) - tan²(x/2) =1

Starting with the left side

2/(1+cosx)   - tan²(x/2)

(1+cosx)/2=cos²(x/2)

Therefore 2/(1+cosx)=1/cos²(x/2) = sec²(x/2)

sec²(x/2) = tan²(x/2)

And sec²A-tan²A=1

Therefore sec²(x/2) - tan²(x/2) =1