Trigonometry formulas (1)

Important Trigonometry formulas-

Trigonometry is very important part if mathematics ,this is used in different fields of different studies like in physics, engineering , etc.

Different types of problems in Trigonometry  can be solved using trigonometry formulas. These problems may include trigonometric ratios (sin, cos, tan, sec, cosec and cot),and many other  problems.

These formulas are very important in mathematics  in trigonometry  and will help the students of all Classes to score good marks in trigonometry . Following are some formulas used in trigonometry.

$\;\;\bullet \displaystyle \sin(-x) = \sin(x)$

$\;\;\bullet \displaystyle \cos(-x) = \cos(x)$

$\;\;\bullet \sin^2(x) + \cos^2(x) = 1$

$\;\;\bullet \displaystyle \tan (x)= \frac{\sin(x)}{ \cos(x)}$

$\;\;\bullet \displaystyle \cot(x) = \frac{ \cos(x)}{\sin(x)} = \frac{1}{\tan(x)}$

$\;\;\bullet \displaystyle \sec(x) =\frac{ 1}{\cos(x)}$

$\;\; \bullet \displaystyle\csc(x) =\frac{1}{\sin(x)}$

$\;\;\bullet \displaystyle\sin^2(x) + \cos^2(x) = 1$

$\;\;\bullet \displaystyle\tan^2(x) + 1 = \sec^2(x)$

$\;\;\bullet 1 + \cot^2(x) = \csc^2(x)$

$\;\;\bullet \displaystyle \sin(A+B) = \sin A \cos B  + \cos  A \sin B$

$\;\;\bullet \displaystyle\cos(A+B) = \cos A \cos B  - \sin A \sin B$

$\;\;\bullet \displaystyle \sin(A-B) = \sin A \cos B  - \cos A \sin B$

$\;\;\bullet \displaystyle\cos(A-B) = \cos A \cos B + \sin A \sin B$

$\;\;\bullet \displaystyle \cos C+ \cos D=2\cos \frac{(C+D)}{2}\cos  \frac{(C-D)}{2}$

$\;\;\bullet \displaystyle \cos C- \cos D=-2\sin \frac{(C+D)}{2}\sin  \frac{(C-D)}{2}$

$\;\;\bullet \displaystyle \sin C+ \sin D=2\sin \frac{(C+D)}{2}\cos  \frac{(C-D)}{2}$

$\;\;\bullet \displaystyle \sin C- \sin D=2\cos \frac{(C+D)}{2}\sin  \frac{(C-D)}{2}$

$\;\;\bullet \displaystyle\sin 2x = 2\sin x\cos x\; \;or \;\; \frac{2 \tan x}{1+\tan^2x}$

$\;\;\bullet \displaystyle\cos 2x = \cos^2 x - \sin^2 x\;\; \;or\; 1- 2\sin^2 x \;$

$\;\;or \;\;2\cos^2 x - 1\;\; \;or\; \;\; \displaystyle \frac{1-\tan^2 x}{1+\tan^2 x}$

$\;\; \bullet \displaystyle\sin^2 x = \frac{1 - \cos 2x}{2}$

$\;\; \bullet \displaystyle\cos^2 x = \frac{1 + \cos 2x}{2}$

$\;\;\bullet \displaystyle \tan(x+y) = \frac{\tan(x) + \tan(y)}{1 -\tan(x)\tan(y)}$

$\;\;\bullet \displaystyle \tan(x-y) = \frac{\tan(x) - \tan(y)}{1 +\tan(x)\tan(y)}$

$\;\;\bullet \displaystyle \tan 2x = \frac{2\tan x}{1-\tan^2 x}$

$\;\; \bullet \displaystyle \cot(x+y) = \frac{\cot x\cot y-1}{\cot x  + \cot y}$

$\;\; \bullet \displaystyle \cot(x-y) = \frac{\cot x\cot y+1}{\cot y - \cot x}$

$\;\;\bullet \displaystyle \sin 3x =3\sin x-4\sin^3 x$

$\;\;\bullet \displaystyle \cos 3x=4 \cos^3 x-3\cos x$