Question

Question #c2994

Answer 1

See explanation

Explanation:

Assuming you want to verify the identity

`1/sin(x)-sin(x)=cos(x)/tan(x)`

(A slight change regarding signs on the LHS)

We will use

• `cos^2(x)+sin^2(x)=1`
• `tan(x)=sin(x)/cos(x)`

`RHS=cos(x)/tan(x)`

`=cos(x)/(sin(x)/cos(x))`

`=cos^2(x)/(sin(x))`

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

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

`=1/sin(x)-sin(x)=LHS`