Question

Simplify the trigonometric expression:

csc(x) - sin(x) / cot(x)

Answer 1

cos(x)

Explanation:

Answer 2

`\\ sin^2 \alpha +cos^2 \alpha =1 ~~~~~~~~~cos^2x=1-sin^2x\\ csc \alpha = (1)/(sin \alpha ) \\ cot \alpha = (cos \alpha )/(sin \alpha ) \\ \\ \\ (csc(x) - sin(x) )/(cot(x)) = \\ = ( (1)/(sin(x)) - sin(x) )/((cos \alpha )/(sin \alpha ) ) \\\ = ( sin(x)((1)/(sin(x)) - sin(x)) )/((sinxcos \alpha )/(sin \alpha ) ) \\ = (1-sin^2(x))/(cos(x)) \\ = (cos^2(x))/(cos(x)) \\ =(cosx)cos(x))/(cos(x)) \\ =cos(x)`