What is tan(pi/2-x/2) ?

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

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simplify tan(pi/2-x/2)

simplify

tan (\frac{π}{2} - \frac{x}{2})

cot (\frac{x}{2})

Solution steps

tan (\frac{π}{2} - \frac{x}{2})

Rewrite using trig identities

= \frac{cos ( \frac{x}{2} )}{sin ( \frac{x}{2} )}

Use the basic trigonometric identity:

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

= cot (\frac{x}{2})

sin (\frac{π}{2} + arccos (x))

sin (w (t - \frac{π}{w}))

- \frac{sin ( - nπ )}{n ^{2}}

- sin (x + \frac{π}{3})

tan (- 4 x)