Conversion Formulas
(i) Degree to Radian
Radian measure =  $\frac{\pi }{180}$ × Degree measure
(ii) Radian to Degree
Degree measure = $\frac{180}{\pi }$ × Radian measure

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Trigonometric Identities
1. $\sin x\csc x=1$
2. $\cos x\sec x=1$
3. $\tan x\cot x=1$
4. $\cos^{2}x+\sin^{2}x=1$
5. $\sec^{2}x=1+\tan^{2}x$
6. $\csc^{2}x=1+\cot^{2}x$
7. $\cos (x+y)=\cos x\cos y-\sin x\sin y$
8. $\cos (x-y)=\cos x\cos y+\sin x\sin y$
9. $\sin (x+y)=\sin x\cos y+\cos x\sin y$
10. $\sin (x-y)=\sin x\cos y-\cos x\sin y$
11. $\tan \left ( x+y \right )=$ $\large \frac{\tan x+\tan y}{1-\tan x\tan y}$
12. $\tan \left ( x-y \right )=$ $\large \frac{\tan x-\tan y}{1+\tan x\tan y}$
13. $\cot \left ( x+y \right )$ $\large =\frac{\cot x\cot y-1}{\cot y+\cot x}$
14. $\cot \left ( x-y \right )$ $\large =\frac{\cot x\cot y+1}{\cot y-\cot x}$
15. $\cos 2x$ $=\cos ^{2}x-\sin^{2}x$ $=2\cos^{2}x-1$ $=1-2\sin^{2}x$ $\large =\frac{1-\tan^{2}x}{1+\tan^{2}x}$
16. $ \sin 2x=2\sin x\cos x$ $\large =\frac{2\tan x}{1+\tan^{2}x}$
17. $\tan 2x$ $\large =\frac{2\tan x}{1-\tan^{2}x}$
18. $\sin 3x=3\sin x-4\sin^{3}x$
19. $\cos 3x=4\cos^{3}x-3\cos x$
20. $\cos x+\cos y$  $ =2\cos\left ( \frac{x+y}{2} \right )\cos\left ( \frac{x-y}{2} \right )$
21. $\cos x-\cos y$ $ =-2\sin\left ( \frac{x+y}{2} \right )\sin\left ( \frac{x-y}{2} \right )$
22. $\sin x+\sin y$ $ =2\sin\left ( \frac{x+y}{2} \right )\cos\left ( \frac{x-y}{2} \right )$
23. $\sin x-\sin y$ $ =2\cos\left ( \frac{x+y}{2} \right )\sin\left ( \frac{x-y}{2} \right )$

Solving equations, sin x = 0, cos x = 0 and tan x = 0
$\sin x=0$  ⇒ x = nπ, n∈I
$\cos x=0$  ⇒  $x=\left ( 2n+1 \right )\frac{\pi }{2}$, n∈I
$\tan x=0$  ⇒  x = nπ, n∈I

For all real numbers x and y
$\sin x=\sin y$  implies $x=n\pi +(-1)^{n}y$
$\cos x=\cos y$  implies $x=2n\pi\pm y$
$\tan x=\tan y$  implies $x=n\pi+y$