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SSC CPO 2023 PYQ — Question 114

SSC CPO - 04 Oct 2023 - Shift 1 • Quantitative Aptitude • Q114

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In ΔABC, ∠B = 90° and AB : BC = 1 : 2. The value of cos A + tan C is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 2+525\frac{2+\sqrt5}{2\sqrt5}

Given that

In ΔABC, ∠B = 90° and AB : BC = 1 : 2

⇒ AC2 = 12 + 22 = 5

⇒ AC = √5

cos A = AB/AC = 1/√5

tan C = AB/BC = 1/2

Hence, the value of  cos A + tan C = 1/√5 + 1/2 = 2+525\frac{2+\sqrt5}{2\sqrt5}