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# Notes | EduRev

## Class 10 : Notes | EduRev

The document Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
All you need of Class 10 at this link: Class 10

Q.1. Evaluate the following:
(i) sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan2 45° + cos2 30° − sin2 60°

Sol. (i) sin 60° cos 30° + sin 30° cos 60°

(ii) 2 tan2 45° + cos2 30° - sin2 60°

numerator and denominator by (1 - √3 )]

On multiplying numerator and denominator by (3√3 - 4) we get

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

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

(A) tan 90°
(B) 1
(C) sin 45°
(D) 0

(iii) sin 2A = 2 sin A is true when A =
(A) 0°
(B) 30°
(C) 45°
(D) 60°

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

Sol.

Correct option is (A)

Correct option is (D)
(Hi) sin 2A = 2 sin A, for A = 0°
LHS sin 2 A = sin 2 x 0 = sin 0° = 0
RHS 2 sin A = 2 sin 0° = 2 x 0 = 0
Correct option is (A)

Correct option is (C)

Q.3. If tan (A + B) = 3 and tan (A − B) =
Sol. tan (A + B) = √3 ⇒ tan (A + B) = tan 60°
⇒ A + B = 60° ...(i)

⇒ A - B = 30°   ......(ii)
Adding (i) and (ii), we get
2A = 90°
⇒ A = 90°/2 = 45°
From (i), 45° + B = 60°
⇒ B = 60° - 45° = 15°
Hence, ∠A = 45°, ∠B = 15°

Q.4. State whether the following are true or false. Justify your answer.
(i) sin (A + B) sin A + sin B.
(ii) The value of sin θ increases as θ increases.
(iii) The value of cos θ increases as θ increases.
(iv) sin θ = cos θ for all values of θ.
(v) cot A is not defined for A = 0°.
Sol. (i) Let, A = 60° and B = 30°
Then, LHS = sin(60° + 30°) = sin 90° = 1
and RHS = sin A + sin B - sin 60° + sin 30°

∴ LHS ≠ RHS     (False)
(ii) sin 0° = 0,

∴ Value of sin 0 increases as 0 increases     (True)
(iii) cos 0° = 1,

∴  Value of cos θ decreases as θ increases      (False)

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