Verified by Ajay Kumar
If \(\cos A=\frac{12}{13}\) and \(\sin B=\frac{5}{13}\), find \(\sin A\cos B+\cos A\sin B\).
\(\frac{60}{169}\)
\(\frac{13}{169}\)
\(\frac{120}{169}\)
\(\frac{5}{13}\)
Answer: C
Using \(\sin A\cos B+\cos A\sin B=\sin(A+B)\), find the missing ratios. Since \(\cos A=\frac{12}{13}\), \(\sin A=\frac{5}{13}\). Since \(\sin B=\frac{5}{13}\), \(\cos B=\frac{12}{13}\). Therefore, \(\frac{5}{13}\\times\frac{12}{13}+\frac{12}{13}\\times\frac{5}{13}=\frac{120}{169}\). Trick: Use the \(5\text{-}12\text{-}13\) right-triangle ratios.
यदि \(\cos A=\frac{12}{13}\) और \(\sin B=\frac{5}{13}\), तो ज्ञात कीजिए \(\sin A\cos B+\cos A\sin B\)।
\(\frac{60}{169}\)
\(\frac{13}{169}\)
\(\frac{120}{169}\)
\(\frac{5}{13}\)
उत्तर: C
सूत्र \(\sin A\cos B+\cos A\sin B=\sin(A+B)\) का प्रयोग करें। \(\cos A=\frac{12}{13}\) से \(\sin A=\frac{5}{13}\) और \(\sin B=\frac{5}{13}\) से \(\cos B=\frac{12}{13}\) मिलता है। अतः \(\frac{5}{13}\\times\frac{12}{13}+\frac{12}{13}\\times\frac{5}{13}=\frac{120}{169}\)। ट्रिक: \(5\text{-}12\text{-}13\) समकोण त्रिभुज के अनुपात का प्रयोग करें।
Community answers
Votes use a first-party browser cookie to help prevent repeat votes. Votes indicate helpfulness, not correctness.
No community answers yet. Be the first to share how you solved it.
Share your solution
Help other learners understand the steps. Your answer will be reviewed before it appears.