cos2 15° का मान क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 4)
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  1. \(\left( {2 + \sqrt 3 } \right)\)
  2. \(\frac{{\left( {2 + \sqrt 3 } \right)}}{4}\)
  3. \(\frac{{\left( {2 + \sqrt 3 } \right)}}{2}\)
  4. \(\frac{{\left( {1 + \sqrt 3 } \right)}}{2}\)

Answer (Detailed Solution Below)

Option 2 : \(\frac{{\left( {2 + \sqrt 3 } \right)}}{4}\)
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Detailed Solution

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प्रयुक्त सूत्र:

Cos 2A = 2Cos 2 A - 1

गणना:

सूत्र के अनुसार, 

⇒  Cos 2A = 2Cos2  A - 1

⇒  माना A = 15

⇒ Cos 30 = 2Cos2 15 - 1

⇒ \(\frac{\sqrt3} {2} +1 = 2cos^2 15\)

⇒ \( 2cos^2 15 = \frac{\sqrt3+2} {2}\)

⇒ \( cos^2 15 = \frac{\sqrt3+2} {4}\)

⇒ अतः, विकल्प 2 सही है

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