SarkariPYQ

SSC CGL 2024 PYQ — Question 52

SSC CGL - 23 Sep 2024 - Shift 1 • Quantitative Aptitude • Q52

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The value of θ, when 3{\sqrt{3} } cosθ + sinθ = 1 ( 1 ≤ 0 ≤ 90° )

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 90°.

√3cosθ + sinθ = 1

⇒ √3cosθ = 1 – sinθ

Squaring both the sides

⇒ 3cos2θ = 1 + sin2θ – 2sinθ

⇒ 3 – 3sin2θ = 1 + sin2θ – 2sinθ

⇒ 2sin2θ – sinθ – 1 = 0

⇒ 2sin2θ – 2sinθ + sinθ – 1 = 0

⇒ 2sinθ(sinθ – 1) + 1(sinθ – 1) = 0

⇒ (2sinθ + 1) (sinθ – 1) = 0

⇒ sinθ = 1 or -1/2

∴ θ = 90°