Prove the following identitie 21 Cos X Tan2 X2 1 Prove th

Prove the following identitie

2/1 + Cos X - Tan^2 X/2 = 1 Prove the following identities.

Solution

2/(1+cosx) - tan²(x/2)=1

Starting with the left side

cos²(x/2)=(1+cos x)/2

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

sec²(x/2) - tan²(x/2) = 1

2/(1+cosx) - sin²x/(1+cosx)²