Question 1201965
prove that -sin(x)-cos(x)cot(x)=-csc(x) is an identity

-sin(x)-cos(x)cot(x)

{{{-sin(x)-(cos(x)cos(x))/sin(x)}}}

LCM

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

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

{{{( -sin^2(x)- 1+sin^2(x))/sin(x)}}}....sin^2(x) cancel off

{{{(-1/sin(x))}}}

-cosec(x)

PROVED