यदि sin (5x - 25°) = cos(5y + 25°) है, जहाँ 5x - 25° और 5y + 25° न्यूनकोण हैं, तो (x + y) का मान क्या है?

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SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 3)
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  1. 50°
  2. 40°
  3. 18°
  4. 16°

Answer (Detailed Solution Below)

Option 3 : 18°
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दिया गया है:

sin (5x - 25°) = cos(5y + 25°) है, जहाँ 5x - 25° और 5y + 25° न्यूनकोण हैं,

प्रयुक्त अवधारणा:

Sinθ = cos (90°- θ)

गणना:

प्रश्न के अनुसार,

sin (5x - 25°) = cos(5y + 25°)

⇒ sin (5x - 25°) = sin 90 - (5y + 25°)

⇒ (5x - 25°) = 90° - (5y + 25°) 

⇒ 5x + 5y =  90

⇒ x + y =  90/5

⇒ x + y =  = 18° 

∴ सही विकल्प 3 है।

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