Question

Prove that sin6x + sin4x - sin2x = 4cosx.sin2x.cos3x

Answer 1

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Answer 2

sin6x + sin4x - sin2x = 4cosx.sin2x.cos3x

Step-by-step explanation:

Given that,

L.H.S. = sin6x + sin 4x -sin2x

So,

R.H.S.  = 2sin{(6x+4x)/2}. cos{(6x-4x)/2} - sin2x

= 2sin5x.cosx - 2sinx.cosx

= 2cosx (sin5x-sinx)

= 2cosx.2cos{(5x+x)/2} sin{(5x-x)/2}

= 4cosx.sin2x.cos3x

Therefore,

sin6x + sin4x - sin2x = 4cosx.sin2x.cos3x

Learn more: Trigonometry

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