 ## Trigonometry Formulas For Class 10

Trigonometry is an important part of math. Trigonometry is important in terms of board examination. Therefore, to solve the problems of trigonometry, it is necessary to remember the formulas. For this reason, in this article of All Trigonometry Formulas For Class 10, 11, 12, we have shown how to remember through logic.

### Trigonometric Ratio

In a right-angled triangle, the opposite side of a given angle is perpendicular, the opposite side of the right angle is the hypotenuse and the third side is the base.

In \,\Delta ABC, \\ \angle = 90 \degree\, ,\angle C = \theta
\therefore The \,side\, AC\, is\, the\, hypotenuse\, , \\ AB \,is\, perpendicular\, \\ and\, BC\, is\, the\, base.

From the Pythagoras theorem,

## Relationship between arms and angles

Finding the formulas of cosec, sec, and a cot can be obtained by reversing the formulas of sin, cos, and tan.

This means that the formula of cosec will be the inverse of sin, the formula of sec will be the inverse of sec, the formula of cot will be inverse of tan. The numerator is replaced by the numerator and denominator.

\sin \theta = \frac{opposite}{hypotenus} = \frac{AB}{AC} = \frac{1}{cosec \theta}
\cos \theta = \frac{Ajacent}{hypotenus} = \frac{BC}{AC} = \frac{1}{sec \theta}
\tan \theta = \frac{opposite}{Adjacent} = \frac{AB}{BC} =\frac{1}{cot \theta}
\sin \theta = \frac{1}{cosec\theta} \Rightarrow \, \cosec \theta = \frac{1}{sin\theta}
\cos \theta = \frac{1}{sec\theta} \Rightarrow \,\sec \theta = \frac{1}{cos \theta}
\tan \theta = \frac{sin \theta}{cos \theta} \Rightarrow \,\cot \theta = \frac{cos \theta}{sin \theta}

#### Ratios Of Particular Angle Trigonometry Formulas For Class 10

The ratio formula of trigonometry is very important from the point of view. Which is important for all classes of students. In The Ratio Trigonometry Formulas For Class 10, you can remember sin, cos, and tan value. and the other three are opposit like this sin is to Reverse cosec. cos is Reverse to sec and tan Reverse to cot

### The trigonometrical function of the sum

There are definite relations between trigonometric functions of two angles of a triangle.

In this article, “Trigonometry Formulas For Class 10” of math is given. It is based on these relations, especially their sum and difference.

\sin \left ( A \dotplus B \right ) = \sin A \, \cos B \dotplus \cos A \, \sin B
\sin \left ( A – B \right ) = \sin A \, \cos B – \cos A \, \sin B
\cos \left ( A \dotplus B \right ) = \cos A \, \cos B – \sin A \, \sin B
\cos \left ( A – B \right ) = \cos A \, \cos B \dotplus \sin A \, \sin B

### The Trigonometrical function of different

\ tan \left ( A \dotplus B \right ) = \frac{\tan A \dotplus tanB}{1 \dotplus \tan A \,\tan B }
\ tan \left ( A – B \right ) = \frac{\tan A – tanB}{1 \dotplus \tan A \,\tan B }
\ cot \left ( A + B \right ) = \frac{\cot A \times \cot B -1}{ \cot A \dotplus \cot B }
\ cot \left ( A – B \right ) = \frac{\cot A \times \cot B \dotplus 1}{\cot B – \cot B }

### The Multiplication Of different of two angle

\sin \left (A \dotplus B \right ) \, \sin \left (A – B \right ) = \sin^{2} A -\sin^{2} B \\ = \cos^{2} B – \cos^{2} A
\cos \left (A \dotplus B \right ) \, \cos \left (A – B \right ) = \cos^{2} A -\sin^{2} B \\ = \cos^{2} B – \sin^{2} A

### Trigonometric Functions And Formula

\sin C \dotplus \ sinD = 2\,\frac{\sin \left ( C + D \right )}{2}\frac{\cos \left ( C – D \right )}{2}
\sin C – \ sinD = 2\,\frac{\cos \left ( C + D \right )}{2}\frac{\sin \left ( C – D \right )}{2}
\cos C \dotplus \ cos D = 2\,\frac{\cos \left ( C + D \right )}{2}\frac{\cos \left ( C – D \right )}{2}
\cos C – \ cos D = 2\,\frac{\sin \left ( C + D \right )}{2}\frac{\sin \left ( D – C \right )}{2}
2 \, \sin A \cos B =\sin \left (A \dotplus B \right )\dotplus \sin \left (A – B \right )
2 \, \cos A \sin B =\sin \left (A \dotplus B \right )- \sin \left (A – B \right )
2 \, \sin A \sin B =\cos \left (A – B \right )- \cos \left (A \dotplus B \right )
\sin 2A =2\sin A \, \cos A = \frac{2\, \tan A}{1+tan^{2} A}
\cos 2A = \cos^{2}A-\sin^{2}A=1-2\sin2A
\tan2A =\frac{2\,\tan A}{1-\tan^{2}A}
\cot2A =\frac{\cot^{2} A -1}{\cot A}
\sin A = 2\, \sin \frac{A}{2} \cos \frac{A}{2}

### Sum of squares of angles

sin^{2} A \, \dotplus \sin^{2} A = 1
\sin^{2} A = 1 – sin^{2} A
sin^{2} A \, = 1 – \sin^{2} A
sec^{2} A – tan^{2} A = 1
tan^{2} A = 1 \dotplus sec^{2} A
sec^{2} A = tan^{2} A – 1
cot^{2} A – cosec^{2} A = 1
cot^{2} A = 1 \dotplus cosec^{2} A
cosec^{2} A = cot^{2} A – cosec^{2} A

### Three angle formulas

\sin3A = 3\, \sin A – 4\, \sin3A
\cos3A = 4 \ cos 3A – 3 cos A
\tan 3 A = \frac{3\, tan A -tan3A}{1-3tan^{2}A}
\cot 3 A = \frac{3\, cot3 A -tan3A}{3cot^{2}A – 1}

### Half Angle Identities

\sin \left ( \frac{A}{2} \right ) = \mp \sqrt{\left (\frac{1- cos A}{2} \right )}
\cos \left ( \frac{A}{2} \right ) = \mp \sqrt{\left (\frac{1\dotplus cos A}{2} \right )}
\tan \left ( \frac{A}{2} \right ) = \frac{\sin A}{1 \dotplus \cos A} = = \frac{1-\cos A}{\sin A}

## trigonometry Formulas For Class 10 PDF

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