Question

How do you verify the identity: `(cot(t)-tan(t))/(sin(t)cos(t)) = csc^2 (t) - sec^2 (t)`?

Answer 1

Verify the identity: `(cot t - tan t)/(sin t.cos t)`

Explanation:

`((cos t/sin t) - (sin t/cos t))/(sin t.cos t) =`

=`(cos^2 t - sin^2 t)/(sin^2 t.cos^2 t)` =`1/(sin^2 t) - 1/(cos^2 t) =`

`= csc^2 t - sec^2 t`