Calculus and Trigonometric Functions Quiz

$f'(x)=\frac{\sin x}{1+\cos x}\cdot (3\tan^2x-\tan x)$

$f'(x)=\frac{\sin x}{1+\cos x}\cdot \tan^2x$

$f'(x)=\frac{2\sin^2x}{(1+\cos x)^2}$ (correct)

$f'(x)=\frac{\sin x}{1+\cos x}\cdot (3\tan^2x+\tan x)$

$x=\pi+k\pi, \: k\in \mathbb{Z}$

$x=2\pi+k\pi, \: k\in \mathbb{Z}$

$x=\frac{3\pi}{2}+k\pi, \: k\in \mathbb{Z}$

$x=\frac{\pi}{2}+k\pi, \: k\in \mathbb{Z}$ (correct)

The limit does not exist

The limit is $\infty$ (correct)

The limit is $0$

The limit is $1$