1.

sin 5 x-2sin 3x+ sin xProve that == tan xcossx-cos x

Answer»

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

LHS

=[(sin5x-sin3x)-(sin3x-sinx)]/(cos5x-cosx)

=[(2cos4x.sinx)-(2cos2x.sinx)]/(-2sin3x.sin2x)

=2sinx.(cos4x-cos2x)/(-2sin3x.2sinx.cosx)

=(cos4x-cos2x)/(-2sin3x.cosx)

=(-2sin3x.sinx)/(-2sin3x,cosx)

=(sinx)/(cosx)

=tanx , Proved.



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