Prove that sin5x 2sin3x sinx cos5x cosx tanx
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Prove that sin5x - 2sin3x + sinx / cos5x - cos x is equal to tan x
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(sin5x-2sin3x+sinx)/(cos5x-cosx)
=[{2sin(5x+x)/2cos(5x-x)/2}-2sin3x]/{2sin(5x+x)/2sin(x-5x)/2}
=(2sin3xcos2x-2sin3x)/{2sin3xsin(-2x)}
={2sin3x(cos2x-1)}/{-2sin3xsin2x}
=-(cos2x-1)/sin2x
=(1-cos2x)/sin2x
=2sin²x/2sinxcosx
=sinx/cosx
=tanx (Proved)
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