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SSC CGL 2024 PYQ — Question 65

SSC CGL - 12 Sep 2024 - Shift 2 • Quantitative Aptitude • Q65

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If 7 tan θ = 3, then 7sinθ+5cosθ7sinθ−2cosθ is:{7sin\theta+5cos\theta\over 7sin\theta-2cos\theta}\ is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 8.

Given that, 7 tan θ = 3

⇒ 7sin⁡θcos⁡θ{7\sin\theta \over \cos\theta}  = 3

⇒ 7 sinθ = 3 cosθ

According to the question,

⇒ 7sinθ+5cosθ7sinθ−2cosθ{7sin\theta+5cos\theta\over 7sin\theta-2cos\theta}

⇒ 3cos⁡θ+5cos⁡θ3cos⁡θ−2cos⁡θ{3 \cos\theta+5 \cos\theta\over 3 \cos\theta-2 \cos\theta}

⇒ 8cos⁡θcos⁡θ{8 \cos\theta}\over \cos\theta = 8

Hence the required answer is 8.