Cos^4 a +cos^2 a +sin^2 a *cos^2 a

Question

Cos^4 a +cos^2 a +sin^2 a *cos^2 a

Answer 1

(1+сos2a)²/4+(1+cos2a)/2+(1-cos2a)(1+cos2a)/4=
=(1+2cos2a+cos²2a+2+2cos2a+1-cos²2a)/4=
=(4cos2a+4)/4=4(cos2a+1)/4=cos2a+1=2cos²a