sin 5x -2sin 3x + sin xcos 5x -cos x= tanx40. Prove that

1.	sin 5x -2sin 3x + sin xcos 5x -cos x= tanx40. Prove that
Answer» (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) hit like if you find it useful

Answer»

(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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sin 5x -2sin 3x + sin xcos 5x -cos x= tanx40. Prove that

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