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SSC CPO 2022 PYQ — Question 134

SSC CPO - 9 Nov 2022 - Shift 3 • Quantitative Aptitude • Q134

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What is the value of sin⁡(A+B)sin⁡Acos⁡B?\frac{\sin (A + B)}{\sin A \cos B}?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 1 + cot A tan B.

The value of sin⁡(A+B)sin⁡Acos⁡B\frac{\sin (A + B)}{\sin A \cos B}

⇒ sin⁡AcosB+cosAsinBsin⁡Acos⁡B\frac{\sin A cos B + cos A sin B}{\sin A \cos B}

⇒ 1+cosAsinBsin⁡Acos⁡B1 +\frac{cos A sin B}{\sin A \cos B}

⇒ 1 + (cosA/sinA) (sin B/cosB)

⇒ 1 + cot A tan B