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SSC CGL 2024 PYQ — Question 56

SSC CGL - 10 Sep 2024 - Shift 3 • Quantitative Aptitude • Q56

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If 7 tanθ = 3, and θ is an acute angle, then 5sinθ−cosθ5sinθ+2cosθ5sinθ-cosθ\over{5sinθ+2cosθ} is equal to:

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 8298\over29.

7 tanθ = 3

⇒ tanθ = 3/7 = P/B

By Pythagoras theorem,

⇒ H2 = B2 + P2

here, H = Hypotaneous, B = Base, and P = Perpendicular

Now,

⇒ H2 = 72 + 32

⇒ H2 = 49 + 9

⇒ H2 = 58

⇒ H = √58

Now,

⇒ sinθ = P/H = 3/√58

⇒ cosθ = B/H = 7/√58

The value of 5sinθ−cosθ5sinθ+2cosθ5sinθ-cosθ\over{5sinθ+2cosθ}

⇒ 5×358−7585×358+14585\times {3\over \sqrt58}- {7\over \sqrt58}\over5\times {3\over \sqrt58}+ {14\over \sqrt58}

⇒ 1558−7581558+1458{15\over \sqrt58}- {7\over \sqrt58}\over{15\over \sqrt58}+ {14\over \sqrt58}

⇒ 8582958{8\over \sqrt58}\over{29\over \sqrt58} = 8298\over29