Question #fe5a3

1 Answer
Nov 5, 2017

sec^2(x/2) = (csc^2x)(2-2cosx)

Explanation:

sec^2(x/2) = 1/cos^2(x/2)

Half angle identity forumla = cos^2(a/2)=(1+cos(a))/2

1/(1+cos(a))/2= 2/(1+cos(x)

Then multiply both numerator and denominator by 1-cos(x)

Resulting to

(2-2cos(x))/(1-cos^2(x)

Then with the identity

sin^2=1-cos^2

The final result will be

(2-2cos(x))/(sin^2(x)) = (2-2cos(x))csc^2(x)