Question

The sum of $\tan x+2\tan 2x+2^2\tan 2^{2}x+...n$ terms..

Answer 1

$T_1=\frac{sinx}{cosx}=\frac{si{n}^{2}x}{cosxsinx}=\frac{co{s}^{2}x-cos2x}{cosxsinx}$
$T_1=cotx-2cot2x$
$T_2=2[cot2x-2cot{2}^{2}x]$
$=2cot2x-2^{2}cot{2}^{2}x$
and so on .
$\therefore S_n=cotx-2^{n}cot{2}^{n}x$