Question

Prove? cotx-tanx = cos2x/sinxcosx

Answer 1

See explanation

Explanation:

We want to verify the identity

`cot(x)-tan(x)=cos(2x)/(sin(x)cos(x))`

Remember the identity

• `cos(2x)=cos^2(x)-sin^2(x)`

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

`color(white)(RHS)=(cos^2(x)-sin^2(x))/(sin(x)cos(x))`

`color(white)(RHS)=(cos^2(x))/(sin(x)cos(x))-(sin^2(x))/(sin(x)cos(x))`

`color(white)(RHS)=(cos(x))/(sin(x))-(sin(x))/(cos(x))`

`color(white)(RHS)=cot(x)-tan(x)=LHS`