Question

How do you find the equivalent expression for `tan(x-pi/2)`?

Answer 1

• cot x

Explanation:

`tan (x - pi/2) = (sin (x - pi/2))/(cos (x - pi/2)`
Unit circle and property of complementary arcs give:
`sin (x - pi/2) = - cos x`
`cos (x - pi/2) = sin x`
There for:
`tan (x - pi/2) = - cos x/(sin x) = - cot x`