यदि sin (A - B) = \(\frac{1}{2}\), और sin(A + B) = 1 है, जहाँ A और B धनात्मक न्यूनकोण हैं और A ≥ B, तो A और B क्रमशः हैं:

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SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 04 Aug, 2023 Shift 4)
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  1. 80°, 10°
  2. 60°, 30°
  3. 70°, 20°
  4. 50°, 40°

Answer (Detailed Solution Below)

Option 2 : 60°, 30°
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दिया गया है:

sin (A - B) = \(\frac{1}{2}\),  sin(A + B) = 1

गणना:

 sin (A - B) = \(\frac{1}{2}\)

⇒ sin (A - B) = sin 30° 

⇒  (A - B) = 30°

पुनः,

sin(A + B) = sin 90° 

⇒ (A + B) = 90°

इसलिए,

(A - B) + (A + B) = 90° + 30°

⇒ 2A = 120° 

⇒ A = 60° 

और B = 30°

 ∴ सही विकल्प 2 है

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