Question

prove that =sin5x-2sin3x+sinx÷cos5x-cosx​

Answer 1

(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