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SSC CHSL 2024 PYQ — Question 70

SSC CHSL - 09 July 2024 - Shift 2 • Quantitative Aptitude • Q70

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If tanθ = 747\over4, then the value of 4 sin θ − 3 cos θ4 sin θ + 3 cos θ{4\ sin\ θ\ -\ 3\ cos\ θ}\over{{4\ sin\ θ\ +\ 3\ cos\ θ}} is equal to:

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 252\over5.

We know that,

tanθ = sinθ/cosθ

sinθ/cosθ = 747\over4

So, the value of 4 sin θ − 3 cos θ4 sin θ + 3 cos θ{4\ sin\ θ\ -\ 3\ cos\ θ}\over{{4\ sin\ θ\ +\ 3\ cos\ θ}}

⇒ 4(74cosθ)− 3 cos θ4(74cosθ)+ 3 cos θ{4({7\over4}cosθ) -\ 3\ cos\ θ}\over{{4({7\over4}cosθ) +\ 3\ cos\ θ}}

⇒ 7 sin θ − 3 cos θ7 sin θ + 3 cos θ{7\ sin\ θ\ -\ 3\ cos\ θ}\over{{7\ sin\ θ\ +\ 3\ cos\ θ}}

⇒​​​​​​​ 4 sin θ 10cos θ{4\ sin\ θ\ }\over{{10cos\ θ}} = 4104\over10 = 252\over5