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SSC CGL 2024 PYQ — Question 65

SSC CGL - 19 Sep 2024 - Shift 3 • Quantitative Aptitude • Q65

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If tanθ = 585\over8, then find the value of (1+cosθ)(1−cosθ)(1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ)\over (1+sinθ)(1−sinθ).

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 256425\over64.

Here, tanθ = 5/8 = sinθ/cosθ

Now, (1+cosθ)(1−cosθ)(1+sinθ)(1−sinθ)(1+cosθ)(1−cosθ)\over (1+sinθ)(1−sinθ)

= 1−cos2θ1−sin2θ1 - cos^2θ \over 1 - sin^2θ = sin2θcos2θsin^2θ\over cos^2θ   [∵ sin2θ + cos2θ = 1]

= (5/8)2 = 25/64