Question

How do you prove `csc x - sin x = cos x cot x`?

Answer 1

see below

Explanation:

`cscx-sinx`

`=1/sinx-sinx`

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

`=cos^2x/sinx`

`=cosx*cosx/sinx`

`=cosxcotx`

Answer 2

Please see the proof below

Explanation:

We need

`cscx=1/sinx`

`cos^2x+sin^2x=1`

`cotx=cosx/sinx`

Therefore,

`LHS=cscx-sinx`

`=1/sinx-sinx`

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

`=cos^2x/sinx`

`=cosx*cosx/sinx`

`=cosxcotx`

`=RHS`

`QED`