NCERT Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry on Padhaiwise

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.1#

Exercise 8.1 introduces trigonometric ratios — sine, cosine, tangent, cosecant, secant, and cotangent — defined with respect to the sides of a right-angled triangle. Students learn to find these ratios from given information.

Trigonometric Ratios in right △ABC (right angle at B), for the acute angle A:

Ratio Definition Reciprocal

$\sin A$ $\dfrac{\text{side opposite to } A}{\text{hypotenuse}} = \dfrac{BC}{AC}$ $\cosec A = \dfrac{1}{\sin A}$

$\cos A$ $\dfrac{\text{side adjacent to } A}{\text{hypotenuse}} = \dfrac{AB}{AC}$ $\sec A = \dfrac{1}{\cos A}$

$\tan A$ $\dfrac{\text{side opposite to } A}{\text{side adjacent to } A} = \dfrac{BC}{AB}$ $\cot A = \dfrac{1}{\tan A}$

Ratio	Definition	Reciprocal
$\sin A$	$\dfrac{\text{side opposite to } A}{\text{hypotenuse}} = \dfrac{BC}{AC}$	$\cosec A = \dfrac{1}{\sin A}$
$\cos A$	$\dfrac{\text{side adjacent to } A}{\text{hypotenuse}} = \dfrac{AB}{AC}$	$\sec A = \dfrac{1}{\cos A}$
$\tan A$	$\dfrac{\text{side opposite to } A}{\text{side adjacent to } A} = \dfrac{BC}{AB}$	$\cot A = \dfrac{1}{\tan A}$

1. In △ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine: #

Setup

By Pythagoras Theorem:

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.2#

Exercise 8.2 deals with trigonometric ratios of specific angles: 0°, 30°, 45°, 60°, and 90°. Students use these standard values to evaluate expressions.

Standard Trigonometric Values:

Angle	$0°$	$30°$	$45°$	$60°$	$90°$
$\sin$	$0$	$\tfrac{1}{2}$	$\tfrac{1}{\sqrt{2}}$	$\tfrac{\sqrt{3}}{2}$	$1$
$\cos$	$1$	$\tfrac{\sqrt{3}}{2}$	$\tfrac{1}{\sqrt{2}}$	$\tfrac{1}{2}$	$0$
$\tan$	$0$	$\tfrac{1}{\sqrt{3}}$	$1$	$\sqrt{3}$	Not defined
$\cosec$	Not defined	$2$	$\sqrt{2}$	$\tfrac{2}{\sqrt{3}}$	$1$
$\sec$	$1$	$\tfrac{2}{\sqrt{3}}$	$\sqrt{2}$	$2$	Not defined
$\cot$	Not defined	$\sqrt{3}$	$1$	$\tfrac{1}{\sqrt{3}}$	$0$

1. Evaluate the following: #

(i) sin 60° cos 30° + sin 30° cos 60°

We find $\sin 60° \cos 30° + \sin 30° \cos 60°$:

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.3#

Exercise 8.3 covers Trigonometric Identities. Students express trigonometric ratios in terms of other ratios and evaluate expressions using fundamental identities.

Fundamental Identities:

$\sin^2 A + \cos^2 A = 1$
$1 + \tan^2 A = \sec^2 A$
$1 + \cot^2 A = \cosec^2 A$

1. Express the trigonometric ratios $\sin A$, $\sec A$ and $\tan A$ in terms of $\cot A$. #

Answer

sin A in terms of cot A: