Question

Question #cb109

Answer 1

We apply the identities `cottheta = costheta/sintheta` and `csctheta = 1/sintheta`, to obtain:

`(cosx/sinx)/(1/sinx - sinx) = secx`

`(cosx/sinx)/((1 - sin^2x)/sinx) = secx`

`cosx/sinx*sinx/(1 - sin^2x) = secx`

Now we can apply the identity `cos^2theta + sin^2theta = 1`:

`cosx/sinx * sinx/cos^2x = secx`

Eliminate:

`1/cosx = secx`

And this is true by the reciprocal identity `sectheta = 1/costheta`.

Our identity has been proved :).

Hopefully this helps!