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NDA 2024 Maths · Mathematics · Trigonometric Functions and Identities · easy

If A,B are acute angles with sin A=3/5 and cos B=5/13, then sin (A+B) equals

Single correct option

If A,BA,B are acute angles with sin⁡A=35\sin A=\dfrac35 and cos⁡B=513\cos B=\dfrac5{13}, then sin⁡(A+B)\sin(A+B) equals
  1. A. 3365\dfrac{33}{65}
  2. B. 6365\dfrac{63}{65}
  3. C. 5665\dfrac{56}{65}
  4. D. 1665\dfrac{16}{65}
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Answer: (B) 6365\dfrac{63}{65}

cos⁡A=45\cos A=\frac45, sin⁡B=1213\sin B=\frac{12}{13}. sin⁡(A+B)=35⋅513+45⋅1213=15+4865=6365\sin(A+B)=\frac35\cdot\frac5{13}+\frac45\cdot\frac{12}{13}=\frac{15+48}{65}=\frac{63}{65}. Trap: 3365\frac{33}{65} is sin⁡(B−A)\sin(B-A)-type combination with a sign slip.
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Original question written in the NDA 2024 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake