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SSC CGL 2021 PYQ — Question 57

SSC CGL - 18 Aug 2021 - Shift 2 • Quantitative Aptitude • Q57

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If sin(A + B) = 1 and cos(A - B) = 32\frac{\sqrt{3}}{2}, where A + B ≤\leq 90º and A > B, then the value of 5sin⁡2B + 4tan⁡2A2sinBcosA\frac{5\sin^2B\,+\,4\tan^2A}{2sinBcosA} is:

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 2612\frac{1}{2}.

⇒ sin(A + B) = 1 ⇒ A + B = 90°........(1)

⇒ cos(A - B) = 32\frac{\sqrt{3}}{2} ⇒ A - B = 30° ........(2)

On solving both equations we get, A = 60° and B = 30°

Now, 5sin⁡2B+4tan⁡2A2sinBcosA\frac{5\sin^2B+4\tan^2A}{2sinBcosA} = 5sin230+4tan2602sin30cos60\frac{5sin^230+4tan^260}{2sin30cos60} = 5×14+4×32×12×12\frac{5 \times \frac{1}{4}+4 \times 3}{2 \times \frac{1}{2} \times \frac{1}{2}} = 5×14+1212\frac{5 \times \frac{1}{4}+12}{\frac{1}{2}} = 2612\frac{1}{2}