Question

Prove that:

$cos4\theta -cos4\alpha =8(cos\theta -cos\alpha )(cos\theta +cos\alpha )(cos\theta -sin\alpha )(cos\theta -sin\alpha )$

Answer 1

$cos4\theta -cos4\alpha =2co{s}^{2}2\theta -2co{s}^{2}2\alpha =2(cos2\theta +cos2\alpha )(cos2\theta -cos2\alpha )=2(2co{s}^2\theta -1+1-2si{n}^2\alpha )(2co{s}^2\theta -1-2co{s}^2\alpha +1)=8(co{s}^2\theta -si{n}^2\alpha )(co{s}^2\theta -co{s}^2\alpha )=8(cos\theta -sin\alpha )(cos\theta +sin\alpha )(cos\theta -cos\alpha )(cos\theta +cos\alpha )$