दिए गए व्यंजक का मान ज्ञात कीजिए: cos² 36° + cos 54° ⋅ sin 36° + \(\left(\frac{\tan 26^{\circ}}{\cot 64^{\circ}}\right)\)

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Question

This question was previously asked in

SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 10 Aug, 2023 Shift 3)

Answer 1

प्रयुक्त सूत्र:

Tan (90° - θ) = cot θ

Cos (90° - θ) = sin θ

गणना:

cos2 36° + cos 54° ⋅ sin 36° + \(\left(\frac{\tan 26^{\circ}}{\cot 64^{\circ}}\right)\)

⇒ cos2 36° + cos 54° ⋅ sin 36° + (tan 26°/cot 64°)

⇒ cos2 36° + cos (90° - 36) ⋅ sin 36° + tan 26°/cot (90° - 26)

⇒ cos2 36° + sin 36° ⋅ sin 36° + tan 26°/tan 26°

⇒ cos2 36° + sin² 36° + 1

⇒ 1 + 1 = 2

∴ सही उत्तर 2 है।

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