If tan \(\frac{\pi }{6}\) + sec \(\frac{\pi }{6}\) = x, then find x.

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

Answer (Detailed Solution Below)

Option 1 : √3
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Detailed Solution

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Given:

tan \(\frac{π }{6}\) + sec \(\frac{π }{6}\) = x

Formula used:

Tan 30° = 1/√3

Sec 30° = 2/√3

Calculation:

tan π/6 + sec π/6 = x

⇒ tan 30° + sec 30° = x

⇒ 1/√3 + 2/√3 = x

⇒ x = 3/√3 = √3

∴ The correct answer is √3.

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