# Prove? cotx-tanx = cos2x/sinxcosx

##### 1 Answer

Mar 21, 2018

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#