यदि tan3θ⋅tan7θ = 1 है, जहाँ 7θ एक न्यूनकोण है, तो cot15θ का मान ज्ञात कीजिए।

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SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 3)
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  1. 1
  2. -1
  3. \(-\sqrt3\)
  4. \(\sqrt3\)

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Option 2 : -1
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दिया गया है:

tan3θ⋅tan7θ = 1

प्रयुक्त अवधारणा:

image

गणना:

tan3θ⋅tan7θ = 1

⇒  tan3θ = 1/tan7θ

⇒  tan3θ = cot7θ

⇒  tan3θ = tan(90° - 7θ)

⇒ 3θ = 90° - 7θ

⇒ 10θ = 90°

⇒ θ = 9°

इसलिए, cot15θ = cot135° = - tan45°

⇒ - 1

अभीष्ट उत्तर -1 है।

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