Question

Simplify the expression: cot x sin x - sin quantity pi divided by two minus x. + cos x

Answer 1

$\cot x= \frac{\cos x}{\sin x} \\ \sin ( \frac{ \pi }{2}-x)=\cos x \\ \\ \cot x \sin x-\sin( \frac{ \pi }{2}-x) +\cos x= \\ \frac{\cos x}{\sin x} \sin x- \cos x+ \cos x= \\ \cos x- \cos x+ \cos x = \\ \cos x \\ \\ \ \cot x \sin x-\sin( \frac{ \pi }{2}-x) +\cos x= \cos x$