Question

Cos^(30+theta)-sin^2(30-theta)

Answer 1

Answer:

cos^2(30+theta) -sin^2(30-theta)

= (cos30costheta - sin30sintheta)^2 - (sin30costheta - cos30sintheta) ^2

= (√3costheta/2 - sin theta/2) ^2 - (costheta/2 - √3sintheta/2) ^2

= 3cos^2theta/4 + sin^2theta/4 - √3sinthetacostheta/2 - (cos^theta/4 + 3sin^2theta/4 - √3sinthetacostheta/2)

= 3cos^2theta/4  + sin^2theta/4 - cos^2theta/4 - 3sin^2theta/4

=2cos^2theta/4 - 2sin^2theta/4

=cos^2theta/2 - sin^2theta/2

=1/2cos2theta