## RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8.1 - Free PDF

## FAQs on RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8.1

**1. What are Pythagorean Trigonometric Identities according to RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?**

The Pythagorean Trigonometric Identities are derived from Pythagoras' theorem in trigonometry. The Pythagoras theorem is applied to the right-angled triangle below, yielding:

Opposite^{2} + Adjacent^{2} = Hypotenuse^{2}

Dividing both sides by Hypotenuse^{2}

Opposite^{2}/Hypotenuse^{2} + Adjacent^{2}/Hypotenuse^{2} = Hypotenuse^{2}/Hypotenuse^{2}

sin^{2}θ + cos^{2}θ = 1

One of the Pythagorean identities is this. We can derive two more Pythagorean Trigonometric Identities in the same way.

1 + tan

^{2}θ = sec^{2}θ1 + cot

^{2}θ = cosec^{2}θ

Now you might have a clear understanding of what Pythagorean Trigonometric Identities mean and also their kinds.

**2. What do you contemplate with complementary and supplementary Trigonometric Identities according to RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?**

Complementary angles are a pair of two angles whose sum equals 90°.

sin (90°- θ) = cos θ

cos (90°- θ) = sin θ

cosec (90°- θ) = sec θ

sec (90°- θ) = cosec θ

tan (90°- θ) = cot θ

cot (90°- θ) = tan θ

The supplementary angles are a pair of two angles whose sum equals 180°.

sin (180°- θ) = sinθ

cos (180°- θ) = -cos θ

cosec (180°- θ) = cosec θ

sec (180°- θ)= -sec θ

tan (180°- θ) = -tan θ

cot (180°- θ) = -cot θ

**3. What do you understand by sum and difference Trigonometric Identities?**

The formulas sin(X+Y), cos(X-Y), cot(X+Y), and others are part of the sum and difference identities.

sin (X+Y) = sin X cos Y + cos X sin Y

sin (X-Y) = sin X cos Y - cos X sin Y

cos (X+Y) = cos X cos Y - sin X sin Y

cos (X-Y) = cos X cos Y + sin X sin Y

\[\tan \left ( X+Y \right ) = \frac{\left ( \tan X+\tan Y \right )}{1-\tan X \tan Y }\]

\[\tan \left ( X-Y \right ) = \frac{\left ( \tan X-\tan Y \right )}{1+\tan X \tan Y }\]

**4. How is a Sine Rule described in RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?**

It is the ratio of the side opposite a given angle (in a right-angled triangle) to the hypotenuse is the trigonometric function. The sine rule describes the relationship between a triangle's angles and their corresponding sides. We'll have to use the sine rule to solve non-right-angled triangles. The sine rule can be written as follows for a triangle with sides 'x', 'y', and 'z' and opposite angles X, Y, and Z.

\[\frac{x}{\sin X}=\frac{y}{\sin Y}=\frac{z}{\sin Z}\]

\[\frac{\sin X}{x}=\frac{\sin Y}{y}=\frac{\sin Z}{z}\]

\[\frac{x}{y}=\frac{\sin X}{\sin Y};\frac{y}{z}=\frac{\sin Y }{\sin Z};\frac{x}{z}=\frac{\sin X}{\sin Z}\]

**5. What is a Cosine Rule according to RS Aggarwal Solutions Class 10 Chapter 8 - Trigonometric Identities (Ex 8A) Exercise 8?**

It is the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse is the trigonometric function. When two sides and the included angle of a triangle are given, the cosine rule is used to determine the relationship between the angles and the sides. The sine rule can be written as follows for a triangle with sides 'x', 'y', and 'z' and opposite angles X, Y, and Z.

x

^{2}= y^{2}+ z^{2}- 2yz·cosXy

^{2}= z^{2}+ x^{2}- 2zx·cosYz

^{2}= x^{2}+ y^{2}- 2xy·cosZ