Question

cos^3θ. sin 3θ + sin^3θ cos 3θ =

Answer 1

cos^3θ. sin 3θ + sin^3θ cos 3θ =0
cosθ(cos^2θ*sin3θ + sin^3θ)=0
cos^2θsin3θ+sin3θ=0
(1-sin^2θ)sin3θ +sin3θ=0
sin3θ(-sin^2θ+1)=0
1-sin^2θ=0
sin^2θ=1
sinθ= \[\sqrt{1}\]
therefore θ=90

Answer 2

sin3θ=3sinθ-4sin^3θ
cos3θ=4cos^3θ-3cosθ
cos^3θ. sin 3θ + sin^3θ cos 3θ =cos^3θ(3sinθ-4sin^3θ)+sin^3θ(4cos^3θ-3cosθ)
=3cos^3θsinθ-4sin^3θcos^3θ+4cos^3θsin^3θ-3cosθsin^3θ
=3cos^3θsinθ-3cosθsin^3θ
=3cosθsinθ(cos^2θ-sin^2θ)
=3cosθsinθcos2θ
=3/2*2cosθsinθcos2θ
=3/2sin2θcos2θ