Prove that,
cos(x)(cot(x)+tan(x)) = csc(x) = 1/sin(x)
manipulate the lhs
cos(x){cos(x)/sin(x) + sin(x)/cos(x)}
cos(x){cos^2(x)/[cos(x)sin(x)] + sin^2(x)/[cos(x)sin(x)]}
cos(x){cos^2(x) + sin^2(x)}/[cos(x)sin(x)]
cos(x){1}/[cos(x)sin(x)]
1/sin(x) = rhs
Q.E.D.