ΔXYZ में, Y पर समकोण है, यदि sin X = \(\frac{1}{2}\), cos X cos Z + sin X sin Z का मान ज्ञात कीजिए। 

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 3)
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  1. \(\frac{\sqrt3}{2}\)
  2. \(\frac{\sqrt3}{4}\)
  3. \(\frac{2}{\sqrt3}\)
  4. \(\sqrt3\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{\sqrt3}{2}\)
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Detailed Solution

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प्रयुक्त सूत्र:

cos X cos Z + sin X sin Z = (cos Z - X)

गणना:

 sin X = \(\frac{1}{2}\) = 30° 

X =  30°,  = 90°

z = 60°

(cos Z - X) = cos 60° - 30°

cos 30° = \(\frac{\sqrt3}{2}\)

∴ सही विकल्प 1 है। 

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