Question 955024
it appears this one can be solve by converting everything to sines and cosines and secants and cosecants.


here's how:


work with the left side of the equation.


the expression on the left side of the equation is :


{{{(csc(x)-csc(x)cos^2(x))/(sin(x)tan(x))}}}


you can factor out {{{csc(x)}}} in the numerator to get:


{{{csc(x) * (1 - cos^2(x)) / (sin(x) * tan(x))}}}


since {{{ 1 - cos^2(x))}}} is equal to {{{sin^2(x)}}}, your expression becomes:


{{{(csc(x) * sin^2(x)) / (sin(x) * tan(x))}}}


since {{{sin^2(x) / sin(x)}}} is equal to {{{sin(x)}}}, your expression becomes:


{{{(csc(x) * sin(x)) / tan(x)}}}


since {{{csc(x) = 1/sin(x)}}} and since {{{sin(x) / sin(x)}}} is equal to 1, your expression becomes:


{{{1 / tan(x)}}}.


since {{{ 1 / tan(x)}}} is equal to {{{cot(x)}}}, then your expression becomes:


{{{cot(x)}}}


since the right side of your equation is also equal to {{{cot(x)}}}, you are done and the identity has been proven.