How do I simplify the trigonometric function? sin4(α) − cos4(α) + cos2(α)

1 Answer
Feb 14, 2018

2sin alpha(cos 3 alpha +cos alpha +sin 3 alpha)

Explanation:

At the most it can be factorised as follows:

sin 4alpha = 2sin 2 alpha cos 2alpha= 4sin alphacos alphacos 2alpha

cos 2alpha - cos 4 alpha= 2 sin 3alpha sin alpha

Putting both of them together it is

2sin alpha(2cos alpha cos 2alpha +sin 3 alpha)

Since
2cos alpha cos 2 alpha = cos 3 alpha +cos alpha

2sin alpha(2cos alpha cos 2alpha + sin 3 alpha)=2sin alpha(cos 3 alpha +cos alpha +sin 3 alpha)