Question

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

Answer 1

Proof below

Explanation:

`(csct+cott)(csct-cott)=csc^2t-cot^2t` (Difference of two squares)
`=1+cot^2t-cot^2t` (Identity: `csc^2x=1+cot^2x`)
`=1`