**Download NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.2 – Introduction to Trignometry**

**1. Evaluate the following:**

**i. sin 60° cos 30° + sin 30° cos 60°**

= x + x

= +

=

= 1

**ii. 2 tan ^{2} 45° + cos^{2} 30° – sin^{2} 60°**

= 2

**iii. **

=

=

=

=

=

=

=

=

**iv. **

=

=

=

=

=

=

=

**v. **

=

=

=

=

**2. Choose the correct option and justify your choice:**

**i. **

**(A) sin 60°****(B) cos 60°****(C) tan 60°****(D) sin 30°**

=

=

=

=

= sin 60°

Therefore, correct option is (A)

**ii. **

**(A) tan 90°****(B) 1****(C) sin 45°****(D) 0**

=

=

=

= 0

Therefore, correct option is (D)

**iii. sin 2A = 2 sin A is true when A =**

**(A) 0****(B) 30°****(C) 45°****(D) 60°**

Putting values in the above equation,

sin 2(0) = 2 sin(0) = 0

Therefore, correct option is (A)

**iv. **

**(A) cos 60°****(B) sin 60°****(C) tan 60°****(D) sin 30°**

=

=

=

==

= tan 60°

Therefore, correct option is (C)

**3. If tan(A + B) = √3 and tan(A – B) = , 0° < A + B ≤ 90°; A>B, find A and B.**

∵ tan(A + B) = √3

∴ A + B = 60° …(i)

∵ tan(A – B) =

∴ A – B = 30° …(ii)

Adding equation (i) and (ii)

2A = 90°

⇒ A = 45°

Subtracting equation (i) and (ii)

2B = 30°

⇒ B = 15°

Therefore, the values of A and B are 45° and 15°

**4. State whether the following are true or false. Justify your answer.**

**i. sin(A + B) = sin A + sin B**

False

Let, A = 30°, B = 60°

LHS = sin(A + B) = sin(30° + 60°)

= sin(90°)

= 1

RHS = sin A + sin B = sin 30° + sin 60°

= +

=

LHS ≠ RHS

**ii. The value of sin θ increases as θ increases**

True, provided 0° ≤ θ ≤ 90°

sin θ =

Consider a triangle with the opposite side of constant length.

As θ is increases, length of hypotenuse decreases, therefore the value of sin θ increases.

**iii. The value of cos θ increases as θ increases**

False, provided 0° ≤ θ ≤ 90°

cos θ =

Consider a triangle with the adjacent side of constant length.

As θ is increases, length of hypotenuse increases, therefore the value of cos θ decreases.

**iv. sin θ = cos θ for all values of θ**

False

For θ = 0°

cos θ = 1

sin θ = 0

Therefore, sin θ ≠ cos θ

**v. cot A is not defined for A = 0°**

True

tan 0° = 0

cot 0° = =

∵ Division by zero is not possible

Therefore, cot A is not defined for A = 0°

**Download NCERT Solutions For Class 10 Maths Chapter 8 Exercise 8.2 – Introduction to Trignometry**

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