Question

How do you prove `(1-csc^2t)/ csc^2t = -1/sec^2t`?

Answer 1

Prove trig expression.

Explanation:

Left side of the equation:
`(1 - 1/sin^2 t)/(1/sin^2 t) = (1 - sin^2 t)/sin^2 t (sin^2 t) = - cos^2 t`.
`(- cos^2 t)` can be written as :`- 1/(1/cos^2t) = - 1/(sec^2 t)`.
Therefor:
`(1 - csc^2 t)/(csc^2 t) = - 1/(sec^2 t)`