## Trigonometry Formulas for class 11

Trigonometry is quite a interesting subject. Here are the useful Trigonometry Formulas for class 11 Maths

Basic Formula

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

$cot(x) = \frac {cos(x)}{sin(x)}$

Reciprocal Identities:

$cosec(x) = \frac {1}{sin(x)}$

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

$cot(x) = \frac {1}{tan(x)}$

$sin(x) = \frac {1}{cosec(x)}$

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

$tan(x) = \frac {1}{cot(x)}$

Pythagorean Identities:

$sin^2(x) + cos^2(x) = 1$

$cot^2x +1 = cosec^2x$

$1+tan^2x = sec^2x$

Trigonometric Ratio’s of Common angles

We can find the values of trigonometric ratio’s various angle

Trigonometry Formula for Complementary and supplementary angles

Sin and cos function

1. $cos(A+B)=cos(A)cos(B)-sin(A)sin(B)$
2. $cos(A-B)=cos(A)cos(B)+sin(A)sin(B)$
3. $cos(\pi /2 -A)=sin(A)$
4. $sin(\pi /2 -A)=cos(A)$
5. $sin(A+B)=sin(A)cos(B)+sin(B)cos(A)$
6. $sin(A-B)=sin(A)cos(B)-sin(B)cos(A)$

Tan and cot functions

If none of the angles x, y and (x + y) is an odd multiple of $\pi /2$

$tan(A+B)=\frac{tan(A)+tan(B)}{1-tan(A)tan(B)}$

$tan(A-B)=\frac{tan(A)-tan(B)}{1+tan(A)tan(B)}$

If none of the angles x, y and (x + y) is an multiple of $\pi /2$

$cot(A+B)=\frac{cot(A)cot(B)-1}{cot(A)+cot(B)}$

$cot(A-B)=\frac{cot(A)cot(B)+1}{cot(B)-cot(A)}$

Some more Trigonometric Functions
Double of x (Double Of Angles)

$cos2x=cos^{^{2}}x-sin^{^{2}}x=2cos^{^{2}}x-1=1-2sin^{^{2}}x=\frac{1-tan^{^{2}}x}{1+tan^{^{2}}x}$
$sin2x=2cos(x)sin(x)=\frac{2tan(x)}{1+tan^{^{2}}x}$
$tan2x=\frac{2tan(x)}{1-tan^{^{2}}x}$

Triple of x ( Triple of Angles)

$sin3x=3sin(x)-4sin^{3}x$
$cos3x=4cos^{3}x-3cos(x)$

$tan(3x)=\frac{3tanx-tan^{^{3}}x}{1-3tan^{^{2}}x}$

Sum and Difference of Angles

$cos(A)+cos(B)=2cos\frac{A+B}{2}cos\frac{A-B}{2}$
$cos(A)-cos(B)=-2sin\frac{A+B}{2}sin\frac{A-B}{2}$
$sin(A)+sin(B)=2sin\frac{A+B}{2}cos\frac{A-B}{2}$
$sin(A)-sin(B)=2cos\frac{A+B}{2}sin\frac{A-B}{2}$

Half Angle Formula

Power Reducing Functions

Trigonometric equations Formula’s

1.$sin x = 0$ implies  $x = n \pi$, where n is any integer<br>
2.$cos x = 0$ implies $x = (2n + 1)(\pi /2)$<br>

1. $sinx =siny$ then $x=n \pi + (-1)^{n}y$ where n is any integer<br>
2. $cosx=cosy$ then $x=2n \pi + y$ or $x=2n \pi – y$ where n is any integer<br>
3. $tanx=tany$ then $x=n \pi +y$ where n is any integer<br>

5.Equation of the form
$sin^2x = sin^2 y, cos^2 x = cos^2 y , tan^2 x = tan^2 y$
General solution is given by
$x = n \pi \pm y$ where n is any integer

6.Equation of the form<br>
|sin x|=1 ,General solution is given by $x= (2n+1) \frac {\pi}{2}$<br>
|cos x|=1,General solution is given by $x=n \pi$<br>

Some basics Tips to solve the trigonometry questions

(1) Always try to bring the multiple angles to single angles using basic formula. Make sure all your angles are the same. Using $sin(2x)$ and $sin(x)$ is difficult, but if you use $sin(2x) = 2 sin(x)cos(x)$, that leaves $sin(x)$ and $cos(x)$, and now all your functions match. The same goes for addition and subtraction: don’t try working with $sin(x+y)$ and $sin (x-y)$. Instead, use $sin(X+Y) = sin(x)cos(y)+cos(x)sin(y)$ so that all the angles match

(2) Converting to sin and cos all the items in the problem using basic formula. I have mentioned sin and cos as they are easy to solve.You can use any other also.

(3)Check all the angles for sums and differences and use the appropriate identities to remove them.

(4) Use Pythagorean identifies  to simplify the equations

(5) Practice and Practice. You will soon start figuring out the equation and there symmetry to resolve them fast