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Class 10 Mathematics by VP Classes

Class 10 : Notes | EduRev

The document Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
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Q.1. Evaluate the following:
(i) sin 60° cos 30° + sin 30° cos 60°
(ii) 2 tan2 45° + cos2 30° − sin2 60°

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Sol. (i) sin 60° cos 30° + sin 30° cos 60°
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(ii) 2 tan2 45° + cos2 30° - sin2 60°
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numerator and denominator by (1 - √3 )]
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On multiplying numerator and denominator by (3√3 - 4) we get
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Q.2. Choose the correct option and justify your choice:
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(A) sin 60°
(B) cos 60°
(C) tan 60°
(D) sin 30°

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(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°

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

Sol. 
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Correct option is (A)
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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)
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 Correct option is (C)

Q.3. If tan (A + B) = 3 and tan (A − B) =  Notes | EduRev
Sol. tan (A + B) = √3 ⇒ tan (A + B) = tan 60°
⇒ A + B = 60° ...(i)
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⇒ 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°
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∴ LHS ≠ RHS     (False)
(ii) sin 0° = 0,
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∴ Value of sin 0 increases as 0 increases     (True)
(iii) cos 0° = 1,
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∴  Value of cos θ decreases as θ increases      (False)
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