Question 969502
cot x=cos x/sin x; csc x=1/sinx

Rewrite in terms of sin x and cos x

(cos x/sin x)-(1/sin x) (cos x +1)

There is a common denominator, sin x

[(cos x-1)/sin x] (cos x +1).  Now, multiply the first term by cos x  and by +1

{(cos^2 x-cos x)/sin x}  + (cos x- 1)/sin x

You have a common denominator of sin x

[cos^2 x- cos x + cos x -1]/sin x

In the numerator, the middle 2 terms disappear, and we have cos^2 x -1 left.  But that is sin^2 x
because sin^2 x + cos ^2 x =1

we have sin^2 x/sin x .  That equals sin x, which is the other side of the equation.