Question:
If \(\sin P = \dfrac{5}{13}\) and \(\cos Q = \dfrac{12}{13}\), find \(\sin P \cos Q + \cos P \sin Q\):
यदि \(\sin P = \dfrac{5}{13}\) और \(\cos Q = \dfrac{12}{13}\) है, तो \(\sin P \cos Q + \cos P \sin Q\) का मान ज्ञात कीजिए:
Options:
- 60/169
- 13/13
- 120/169
- 12/13
- 60/169
- 13/13
- 120/169
- 12/13
Correct Answer: c)
Explanation:
From \(\sin P = \dfrac{5}{13}\), \(\cos P = \sqrt{1 – (5/13)^2} = \dfrac{12}{13}\).
From \(\cos Q = \dfrac{12}{13}\), \(\sin Q = \sqrt{1 – (12/13)^2} = \dfrac{5}{13}\).
Then \(\sin P \cos Q + \cos P \sin Q = \left(\dfrac{5}{13}\right)\left(\dfrac{12}{13}\right) + \left(\dfrac{12}{13}\right)\left(\dfrac{5}{13}\right) = \dfrac{60}{169} + \dfrac{60}{169} = \dfrac{120}{169}\).
\(\cos P = \dfrac{12}{13}\) तथा \(\sin Q = \dfrac{5}{13}\).
\(\sin P \cos Q + \cos P \sin Q = \left(\dfrac{5}{13} \times \dfrac{12}{13}\right) + \left(\dfrac{12}{13} \times \dfrac{5}{13}\right) = \dfrac{60}{169} + \dfrac{60}{169} = \dfrac{120}{169}\)।