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

**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__

- $cos(A+B)=cos(A)cos(B)-sin(A)sin(B)$
- $cos(A-B)=cos(A)cos(B)+sin(A)sin(B)$
- $cos(\pi /2 -A)=sin(A)$
- $sin(\pi /2 -A)=cos(A)$
- $sin(A+B)=sin(A)cos(B)+sin(B)cos(A)$
- $sin(A-B)=sin(A)cos(B)-sin(B)cos(A)$

__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__

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

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

$tan2x=\frac{2tan(x)}{1-tan^{^{2}}x}$

__Triple of x__

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

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

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

**Some other Important functions**

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

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

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

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

**Half Angle Formula**

**Pythagoras Identities in Radical form**

**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>

- $sinx =siny$ then $x=n \pi + (-1)^{n}y$ where n is any integer<br>
- $cosx=cosy$ then $x=2n \pi + y$ or $x=2n \pi – y$ where n is any integer<br>
- $tanx=tany$ 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 sinX is difficult, but if you use sin2X = 2sin(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 sinX. 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

Download all the trigonometry Formula below

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