Question:
If \(\sin A = 3/5\) and \(\cos B = 12/13\), find the value of \(\sin A \cos B + \cos A \sin B\):
यदि \(\sin A = 3/5\) और \(\cos B = 12/13\) है, तो \(\sin A \cos B + \cos A \sin B\) का मान ज्ञात कीजिए:
Options:
- 56/65
- 36/65
- 60/169
- 24/65
- 56/65
- 36/65
- 60/169
- 24/65
Correct Answer: a)
Explanation:
\(\cos A = \sqrt{1 – (3/5)^2} = 4/5\) and \(\sin B = \sqrt{1 – (12/13)^2} = 5/13\).
\(\sin A \cos B + \cos A \sin B = \left(\dfrac{3}{5} \times \dfrac{12}{13}\right) + \left(\dfrac{4}{5} \times \dfrac{5}{13}\right) = \dfrac{36}{65} + \dfrac{20}{65} = \dfrac{56}{65}\).
\(\cos A = 4/5\) और \(\sin B = 5/13\)।
\(\sin(A + B) = \dfrac{3}{5} \times \dfrac{12}{13} + \dfrac{4}{5} \times \dfrac{5}{13} = \dfrac{36 + 20}{65} = \dfrac{56}{65}\)।