NDA 2 2025 Maths, question 25

Topic: Trigonometry

Passage · Q25 to Q26

Let $\sin A+\sin B=p$ and $\cos A+\cos B=q$ .

Q25

What is $\frac{p}{q}$ equal to?

(a) $\tan \left( \frac{A-B}{2} \right)$
(b) $\cot \left( \frac{A-B}{2} \right)$
(c) $\tan \left( \frac{A+B}{2} \right)$ Correct answer
(d) $\cot \left( \frac{A+B}{2} \right)$

Solution.

Answer: (c) $\tan \left( \frac{A+B}{2} \right)$

Sum-to-product identities give p=2 sin((A+B)/2) cos((A−B)/2) and q=2 cos((A+B)/2) cos((A−B)/2).
Their ratio is tan((A+B)/2), whenever the original denominator q is nonzero.