Question

How do you verify `cscx-sinx=cosxcotx`?

Answer 1

Let's start by stating the identities that will be important to this problem:

Explanation:

The reciprocal identity (1): `cscx = 1/sinx`

The quotient identity (1): `cotx = cosx/sinx`

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

Placing the left side on a common denominator:

`1/sinx - sin^2x/sinx = cos^2x/sinx`

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

Applying the Pythagorean identity `cos^2x + sin^2x = 1`, we get:

`cos^2x/sinx = cos^2x /sinx`

Hopefully this helps!