जर Sin θ = \(\frac{4}{5}\) , tan θ - Cot θ चे मूल्य शोधा.

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SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 2)
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  1. \(\frac{5}{12}\)
  2. \(\frac{7}{9}\)
  3. \(\frac{7}{12}\)
  4. \(\frac{7}{8}\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{7}{12}\)
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Detailed Solution

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दिलेल्याप्रमाणे:

Sin θ = 4/5

वापरलेले सूत्र:

tan θ = P/B ; cot θ = B/P

पायथागोरियन प्रमेयानुसार:

⇒ H 2 = P 2 + B 2

येथे, P = लंब ; B = पाया; H = कर्ण

गणना:

Sin θ = 4/5 = P/H

पायथागोरियन प्रमेयानुसार :

⇒ H2 = P2 + B2

⇒ 52 = 42 + B2

⇒ B2 = 52 - 42

⇒ B = √(25 - 16) = √9

⇒ B = 3

tan θ - Cot θ

⇒ (P/B) - (B/P)

⇒ (4/3) - (3/4) = (16 - 9)/12

⇒ 7/12

∴ योग्य उत्तर 7/12 आहे.

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