Question 1126914

{{{cos(2x)/sin(x) = csc(x)-2sin(x)}}}


start with left side and arrive to right side 


{{{cos(2x)/sin(x)}}} .....since {{{cos(2x)=cos^2(x) - sin^2(x)}}}, we have


={{{(cos^2(x) - sin^2(x))/sin(x)}}}


={{{cos^2(x)/sin(x) - sin^2(x)/sin(x)}}}


={{{cos^2(x)/sin(x) - sin(x)}}}...............since {{{cos^2(x)=1 - sin^2(x)}}}, we have


={{{(1 - sin^2(x))/sin(x) - sin(x)}}}


={{{1/sin(x)  - sin^2(x)/sin(x) - sin(x)}}}


={{{1/sin(x)  - sin(x) - sin(x)}}}.............since {{{1/sin(x) =csc(x)}}}, we have

={{{csc(x)-2sin(x)}}} -> we have arrived to right side