What is cot(pi/2-x)cos(x) ?

The solution to cot(pi/2-x)cos(x) is sin(x)

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simplify cot(pi/2-x)cos(x)

simplify

cot (\frac{π}{2} - x) cos (x)

sin (x)

Solution steps

cot (\frac{π}{2} - x) cos (x)

Rewrite using trig identities

= \frac{sin ( x )}{cos ( x )} cos (x)

Simplify

\frac{sin ( x )}{cos ( x )} cos (x) : sin (x)

= sin (x)

cos (2 (x + \frac{π}{2}))

sec (\frac{1}{2} π - x)

cos ((x - π) + π)

sin (arccos (\frac{x}{x + 1}))

cot (arccos (\frac{x}{15}))