Question

How do you simplify the expression `secxcotx-cotxcosx`?

Answer 1

`secxcotx - cotxcosx=sinx` for all `x` such that `cosx, sinx != 0`

Explanation:

We will use the following:

• `secx = 1/cosx`
• `cotx = cosx/sinx`
• `sin^2x + cos^2x = 1 => 1 - cos^2x = sin^2x`

`secxcotx - cotxcosx = 1/cosx*cosx/sinx - cosx/sinx*cosx`

`=1/sinx-cos^2x/sinx` (assuming `cosx != 0`)

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

`=sin^2x/sinx`

`=sinx` (assuming `sinx != 0`)