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NDA 2023 Maths · Mathematics · Trigonometric Functions and Identities · medium

If sin A=3/5 and cos B=12/13, where A and B are acute angles, then sin (A+B) equals

Single correct option

If sin⁡A=35\sin A=\dfrac35 and cos⁡B=1213\cos B=\dfrac{12}{13}, where AA and BB are acute angles, then sin⁡(A+B)\sin(A+B) equals
  1. A. 1665\dfrac{16}{65}
  2. B. 3365\dfrac{33}{65}
  3. C. 5665\dfrac{56}{65}
  4. D. 6365\dfrac{63}{65}
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Answer: (C) 5665\dfrac{56}{65}

The acute angles give cos⁡A=45\cos A=\frac45 and sin⁡B=513\sin B=\frac5{13}. Then sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B=35⋅1213+45⋅513=36+2065=5665\sin(A+B)=\sin A\cos B+\cos A\sin B=\frac35\cdot\frac{12}{13}+\frac45\cdot\frac5{13}=\frac{36+20}{65}=\frac{56}{65}. The value 1665\frac{16}{65} is sin⁡(B−A)\sin(B-A) in magnitude-type confusion.
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Original question written in the NDA 2023 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