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SSC CGL 2023 PYQ — Question 58

SSC CGL - 26 July 2023 - Shift 3 • Quantitative Aptitude • Q58

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If tan⁡A=38\tan A = \frac{3}{8}, then the value of 3sin⁡A+2cos⁡A3sin⁡A−2cos⁡A\frac{3 \sin A + 2 \cos A}{3 \sin A - 2 \cos A} is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. −257-\frac{25}{7}.

Given that
tan⁡A=38\tan A = \frac{3}{8}

3sin⁡A+2cos⁡A3sin⁡A−2cos⁡A\frac{3 \sin A + 2 \cos A}{3 \sin A - 2 \cos A}

Dividing the whole equation by cos A we get

3tan⁡A+23tan⁡A−2\frac{3 \tan A + 2 }{3 \tan A - 2 }

Substituting the values of tan A we get,

3×38+23×38−2\frac{3 × \frac{3}{8} + 2 }{3 × \frac{3}{8} - 2 } = −257-\frac{25}{7}

Hence, the value of the given expression is −257-\frac{25}{7}