Methods to Solve Trigonometric Equations

Find the general solution of $\sin x=1$. (Converting it to $\tan \frac{x}{2}$)

Find the general solution of $\frac{1-\cos x}{1+\cos x}=\frac{1}{3}$. (Converting it to $\tan \frac{x}{2}$)

Find the general solution of $\frac{1-\cos x}{1+\cos x}=3$. (Converting it to $\tan \frac{x}{2}$)

Find the general solution of $\frac{1-\cos x}{1+\cos x}=1$. (Converting it to $\tan \frac{x}{2}$)

The number of values of $\theta$ in the interval $\left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$ such that $\theta \ne \frac{n\mathrm{\pi }}{5}$ for $n=0,\pm 1,\pm 2$ and $\tan \theta =\cot 5\theta$ as well as $\sin 2\theta =\cos 4\theta$ is

Find the general solution(s) of the following equation: 

$\sin x-\sin 2x+\sin 3x=0$

Find the general solution of the following equation: $\sin x=\tan x$.

Find the general solution of the following equation: 

$4{\cos }^{2}x-4\sin x-1=0$

Find the general solution of the following equation: 

$\sqrt{2}\mathrm{cosec}x=\cot x+\sqrt{3}$

Find the general solution of the following equation:

$2{\sin }^{2}x+\sqrt{3}\cos x+1=0$

Find the general solution(s) of the following equation:

$\sin 2x+\sin 4x+\sin 6x=0$

Find the general solution of the following equation:

$\tan x+\cot 3x=0$

Find the general solution of the following equation: 

$\cos x-\sin x+1=0$

Find the general solution of the following equation:

$\cos x+\sin x=\cos 2x+\sin 2x$

Find the general solution(s) of the following equation:

$\cos 3x+\cos x-2\cos 2x=0$

Find the general solution(s) of the following equation:

${\sec }^{2}x=1+\tan x$

Find the general solution(s) of the following equation: 

${\tan }^2 x-\sqrt{3}\tan x=0$

Find the general solution(s) of the following equation: 

$2\sin x\cos x=\sin x$