Question

Prove that: Sin2A/1-Cos2A=TanA

Answer 1

Step-by-step explanation:

2sinAcosA/1-2cos^2A +1

= 2sinAcosA/ 2cosA(cosA)

=sinA/cosA

=tanA...

Answer 2

A small mistake, it's  $\dfrac{\sin2A}{1+\cos2A}\ =\ \tan A$

It's simpler to prove it.

$\dfrac{\sin2A}{1+\cos2A}\ =\ \dfrac{2\sin A\cos A}{2\cos^2A}\ =\ \dfrac{\sin A}{\cos A}\ =\ \tan A$

Just recall,

$\sin2A=2\sin A\cos A\quad;\quad 1+\cos2A=2\cos^2A$

And  $\dfrac{\sin2A}{1-\cos2A}\ =\ \cot A$