Question #c2684

2 Answers
Oct 2, 2017

See the proof below

Explanation:

We need

tanx=sinx/cosxtanx=sinxcosx

sin2x=2sinxcosxsin2x=2sinxcosx

Therefore

LHS=(tan(2x)cos2x)/sinxLHS=tan(2x)cos2xsinx

=sin(2x)/cancelcos(2x)*cancelcos(2x)/sinx

=(2cancelsinxcosx)/cancelsinx

=2cosx

=RHS

QED

Oct 2, 2017

L.H.S.
=(tan2xcos2x)/sinx
Using Formula tan2x=(sin2x)/(cos2x)
=(sin2x)/cancel(cos2x)xxcancel(cos2x)/sinx

Using Formula sin2x=2sinxcosx
=(2cancelsinxcosx)/cancelsinx =2cosx#