How do you simplify #cos^2 (theta/2) − sin^2 (theta/2)#?
1 Answer
May 17, 2016
Explanation:
We will use the following identities:
#cos(theta/2)=sqrt((1+costheta)/2)# #sin(theta/2)=sqrt((1-costheta)/2)#
Thus, substituting these into the expression, we get:
#cos^2(theta/2)-sin^2(theta/2)=(sqrt((1+costheta)/2))^2-(sqrt((1-costheta)/2))^2#
#=(1+costheta)/2-(1-costheta)/2#
#=(1+costheta-(1-costheta))/2#
#=(1-1+costheta+costheta)/2#
#=(2costheta)/2#
#=costheta#
