AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C\), if \(3 \sin A+4 \cos B=6\) and \(4 \sin B+3 \cos A=1\), then the \(\angle C\) is
- A \(\frac{\pi}{2}\)
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{6}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{6}\)
Step-by-step Solution
Detailed explanation
\(3 \sin A+4 \cos B=6\)...(i) \(4 \sin B+3 \cos A=1\)...(ii) On adding Eqs. (i) and (ii) after taking square, \(\begin{aligned} & \left(9 \sin ^2 A+24 \sin A \cdot \cos B+16 \cos ^2 B\right)+ \\ & \left(16 \sin ^2 B+24 \sin B \cdot \cos A+9 \cos ^2 A\right)=37\end{aligned}\)…
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