Question

2tanxsinx + 2sinx = tanx +1

Answer 1

I suppose is an eqution you have to solve, so,
\[2\sin x(\tan x+1)=\tan x+1\Rightarrow (\tan x+1)(2\sin x-1)=0\]
\[\tan x+1=0\Rightarrow \tan x=1\Rightarrow x=\frac{\pi}{4}+\pi k\ (k=1,2,\ldots)\]
\[2\sin x-1=0\Rightarrow\sin x=1/2\Rightarrow x=\frac{\pi}{6}+2\pi k\]
And \[x=\frac{5\pi}{6}+2\pi k\]