Question

If $tanx=12/13$ evaluate $\left(2sinxcosx\right)/({cos}^{2}x-si{n}^{2}x)$

Answer 1

$\frac{2\sin x\cos x}{{\cos }^{2}x-{\sin }^{2}x}$

$\Rightarrow \frac{\sin 2x}{\cos 2x}=\tan 2x$

$\tan 2x=\frac{2\tan x}{1-{\tan }^{2}x}$

$=\frac{2\left(12/23\right)}{1-\left(144/169\right)}=\frac{2\times 12\times 13}{25}$

$=\frac{312}{25}$.