Question

Prove the identity
sec²(θ/2)=2/1+cosθ
Thanks for your help!!!!!!

Answer 1

Remember that: \[cos(\theta /2)= \sqrt{\frac{1+cos(\theta)}{2}}\]

Answer 2

we get that from:
\(cos(2\theta) = cos(\theta)*cos(\theta)-sin(\theta)*sin(\theta) = cos^2(\theta)-sin^2(\theta)\), so...
\(cos^2(\theta) = sin^2(\theta)+cos(2\theta)\)
\(cos^2(\theta) = 1-cos^2(\theta )+cos(2\theta)\)
\(cos^2(\theta) = (1+cos(2\theta))/2\)