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

2 Answers
Jun 7, 2018

see below

Explanation:

cscx-sinx

=1/sinx-sinx

=(1-sin^2x)/sinx

=cos^2x/sinx

=cosx*cosx/sinx

=cosxcotx

Jun 7, 2018

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