化简cos^4 a-(1/4)cos^2 2a-(1/2)cos 2a

问题描述:

化简cos^4 a-(1/4)cos^2 2a-(1/2)cos 2a

=1/2*2*cos[(2a-B 2a B)/2]sin[(2a-B-2a-B)/2] =cos[(4a/2]sin[(-2B)/2] =cos2asin(-B) =-cos2asinB cos(a-π/6) sina=4√3

cos^4 a-(1/4)cos^2 2a-(1/2)cos 2a
=[(1/2)(cos2a+1)]²-(1/4)cos²2a-(1/2)cos2a
=(1/4)(cos²2a+2cos2a+1)-(1/4)cos²2a-(1/2)cos2a
=(1/4)cos²2a+(1/2)cos2a+1/4-(1/4)cos²2a-(1/2)cos2a
=1/4