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SSC CGL 2022 PYQ — Question 51

SSC CGL - 06 Dec 2022 - Shift 4 • Quantitative Aptitude • Q51

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If secθ−2cosθ=72secθ - 2cosθ = {{7} \over 2}, where θ is a positive acute angle, then the value of secθ is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 4.

secθ−2cosθ=72secθ - 2cosθ = {{7} \over 2}

⇒ secθ−2/secθ=72secθ - 2/secθ = {{7} \over 2}

⇒ 2Sec2θ - 4 = 7secθ

⇒ 2Sec2θ - 7secθ + 4 = 0

⇒ 2Sec2θ - 8secθ + secθ + 4 = 0

⇒ 2secθ(secθ -  4) + 1(secθ + 4) = 0

⇒ secθ = 4,  -1/2(Neglected)

⇒ secθ = 4