Question #562b9

1 Answer
Dec 3, 2016

To prove 1+tanxtan2x=tan2xcotx-1

LHS=1+tanxtan2x

=1+(tanx xx2tanx)/(1-tan^2x)

=(1-tan^2+2tan^2x)/(1-tan^2x)

=(1+tan^2x)/(1-tan^2x)

=(2-1+tan^2x)/(1-tan^2x)

=(2-(1-tan^2x))/(1-tan^2x)

=2/(1-tan^2x)-(1-tan^2x)/(1-tan^2x)

=(2tanxcotx)/(1-tan^2x)-1

=tan2xcotx-1=RHS

Proved