4sin(420^(@)-alpha)cos(60^(@)+alpha)=

Assertion (A):cos^(2)theta+cos^(2)(60^(@)-theta)+cos^(2)(60^(@)+theta)=(3)/(2)sin alpha-sin(120^(@)-alpha)+sin(120^(@)+alpha)=0

Assertion (A):cos^(2)theta+cos^(2)(60^(@)-theta)+cos^(2)(60^(@)+theta)=(3)/(2)sin alpha-sin(120^(@)-alpha)+sin(120^(@)+alpha)=0

4 sin (420^(@) - alpha ) cos (60^@ + alpha ) =

cos alpha cos(60^(@) - alpha ) cos (60^(@) + alpha ) = 1/4 cos 3 alpha.

cos^(4)alpha+sin^(4)alpha-6sin^(2)alpha cos^(2)alpha=

(cos2 alpha)/(cos^(4)alpha-sin^(4)alpha)-(cos^(4)alpha+sin^(4)alpha)/(2-sin^(2)2 alpha)=

( cos 2 alpha)/( cos^(4) alpha - sin^(4) alpha ) -(cos^(4) alpha + sin^(4) alpha )/(2-sin^(2) 2alpha ) =

sin alpha * sin (60-alpha) sin (60 + alpha) = (1) / (4) * sin3 alpha

Prove that sin^(4) alpha + cos^(4) alpha + 2 sin^(2) alpha cos^(2) alpha = 1 .

Prove that sinalpha*sin(60-alpha)sin(60+alpha) = 1/4*sin3alpha