Question

How do you verify `sec^2((pi/2)-x)-1=cot^2 x`?

Answer 1

Proof below

Explanation:

Identity: `sec^2theta=1+tan^2theta`
`sec^2(pi/2-x)-1=1+tan^2(pi/2-x)-1`
`=tan^2(pi/2-x)`
Identity: `tan(pi/2-theta)=cottheta`
`=cot^2x`