RS Aggarwal Solutions Class 10 Maths Chapter 8 Trigonometric Identities | Updated For 2024

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RS Aggarwal Solutions Class 10 Maths Chapter 8 Trigonometric Identities

RS Aggarwal Solutions Class 10 Maths Chapter 8 Trigonometric Identities – Overview

Trigonometric Identities

Here are the six trigonometric identities mentioned in Chapter 8 of RS Aggarwal Solutions Class 10 Maths.

• Sine Function

The sine function of an angle is the ratio that exists between the opposite side length to that of the hypotenuse of a triangle. It is expressed by:

Sin a = opposite / hypotenuse = CB / CA

• Cos Function

The cos function of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. This function can be represented as:

Cos a = Adjacent / hypotenuse = AB / CA

• Tan Function

The tan/tangent function is the ratio between the length of the opposite side and the length of the adjacent side. It is also possible to represent tan in terms of the values of sine and cos in the form of a ratio. Therefore, the value of a tan function can be equal to:

Tan a = opposite / adjacent = CB / BA

Or Tan a = sin a / cos a

• Secant, Cosecant, and Cotangent Functions

The sine, cos, and tan are three primary functions. Then there are secant, cosecant, and cotangent functions that are the additional trigonometric functions. They can also be defined as the reciprocal of the sine, cos, and tan functions. It is the reciprocal of the sine function, secant is the reciprocal of the cos function, and cotangent is the reciprocal of the cot function.

The formulae for all of these additional functions are:

1. Sec a = 1 / cos a = hypotenuse / adjacent = CA / AB.
2. Cosec a = 1 / sin a = hypotenuse / opposite = CA / CB.
3. Cot a = 1 / tan a = Adjacent / opposite = BA / CB.

Angles in Degrees	0	30	45	60	90	180	270	360
Angles in Radians	0	π/6	π/4	π/3	π/2	π	3π/2	2π
sin	0	1/2	1/√2	√3/2	1	0	-1	0
cos	1	√3/2	1/√2	1/2	0	-1	0	1
tan	0	1/√3	1	√3	∞	0	∞	0
cot	∞	√3	1	1/√3	0	∞	0	∞
csc	∞	2	√2	2/√3	1	∞	-1	∞
sec	1	2/√3	√2	2	∞	-1	∞	1

Fundamental Trigonometric Identities

The trigonometric identities hold true for only a right-angle triangle and are derived from the six main trigonometric ratios.

• Reciprocal Identities

Sin θ = 1 / csc θ or csc θ = 1 / sin θ

Cos θ = 1 / sec θ or sec θ = 1 / cos θ

Tan θ = 1 / cot θ or cot θ = 1 / tan θ

• Pythagorean Identities

Sin 2 a + cos 2 a = 1

1 + tan 2 a = sec 2 a

Cosec 2 a = 1 + cot 2 a

• Ratio Identities

Tan θ = sin θ / cos θ

Cot θ = cos θ / sin θ

• Opposite Angle Identities

Sin (-θ) = – sin θ

Cos (-θ) = cos θ

Tan (-θ) = – tan θ

Cot (-θ) = – cot θ

Sec (-θ) = sec θ

Csc (-θ) = – csc θ

• Complementary Angles Identities

Sin (90 – θ) = cos θ

Cos (90 – θ) = sin θ

Tan (90 – θ) = cot θ

Cot (90 – θ) = tan θ

Sec (90 – θ) = csc θ

Csc (90 – θ) = sec θ

Access RS Aggarwal Solutions Class 10 Maths Chapter 8 Trigonometric Identities Other Important Exercises

RS Aggarwal Solutions Chapter 8 Exercise 8.1

RS Aggarwal Solutions Chapter 8 Exercise 8.2

RS Aggarwal Solutions Chapter 8 Exercise 8.3

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