फद्् कानए sin5x~2sin3x+ sin x =उदाहरण 1705

1.	फद्् कानए sin5x~2sin3x+ sin x =उदाहरण 170553 -0052tanx
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)

फद्् कानए sin5x~2sin3x+ sin x =उदाहरण 170553 -0052tanx

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)