prove that:

sin5x-2sin3x+sinx/cos5x-cosx= tanx

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Solution

= (sin5x + sinx -2sin3x)/(cos5x - cos x)

= (2sin3xcos2x - 2sin3x)/(-2sin3xsin2x)

= 2sin3x(cos2x - 1)/(-2sin3xsin2x)

= cos2x - 1/(-sin2x)

= (1 - 2sin²x) - 1/(-2sinxcosx)

= -2sin²x/-2sinxcosx
=Sinx/cosx =tanx

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