\({\cos^215^{\circ} - \sin^215^{\circ}} \over{\cos^2145^{\circ} + \sin^2145^{\circ}}\)का मान ज्ञात कीजिए

This question was previously asked in
SSC CGL 2023 Tier-I Official Paper (Held On: 26 Jul 2023 Shift 3)
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  1. \(1 \over \sqrt3\)
  2. \(1 \over 1 - \sqrt3\)
  3. \(\sqrt3 \over 2\)
  4. \(2 \over \sqrt3\)

Answer (Detailed Solution Below)

Option 3 : \(\sqrt3 \over 2\)
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Detailed Solution

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प्रयुक्त संकल्पना:

Sin2θ + Cos2θ = 1

Cos 2θ - Sin2θ = Cos2θ

गणना:

\({\cos^215^{\circ} - \sin^215^{\circ}} \over{\cos^2145^{\circ} + \sin^2145^{\circ}}\)

⇒ Cos (2 ×15°)

⇒ Cos 30° = \(\sqrt3 \over 2\)

∴ सही विकल्प 3 है

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