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

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Answer 1 · 2018-02-14T15:01:27

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

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)#