How do you simplify sinxcosx using Trigonometric Identities?

Question

I'm doing a problem where I have to prove the Trigonometric equation, (sinx)(tanx cosx-cotx cosx)=1-2cos²x and I'm distributing the sinx and here's how it looks so far:

sinx tanx sinx cosx - sinx cotx sinx cosx

sinx (sinx/cosx) ?  ?

So I have sinx and cosx, and when I look to see how other people did it, they just subtracted that sinx out of the equation and it's just cosx, and I don't understand why. 

Answer 1

(sinx)(tanx cosx-cotx cosx)=

=sinxcosx(sinx/cosx-cosx/sinx)=

=sinxcosx((sin²x-cos²x)/(sinxcosx))=sin²x-cos²x

= 1-cos²x-cos²x=1-2cos²x