Question

How do you prove `(csc+cot)(csc-cot)=1`?

Answer 1

`csc^2theta=1+cot^2theta` is a trigonometric identity.

Explanation:

`[1]color(white)(XX)(csctheta+cottheta)(csctheta-cottheta)=1`

Property: `(a+b)(a-b)=a^2-b^2`

`[2]color(white)(XX)csc^2theta-cot^2theta=1`

`[3]color(white)(XX)csc^2theta=1+cot^2theta`

This is a trigonometric identity.