AP EAMCET · Maths · Trigonometric Ratios & Identities
In triangle \(A B C\) if \(\cos A \cos B+\sin A \sin B \sin C=1\), then \(\sin A+\sin B+\sin C=\)
- A \(\frac{2+\sqrt{3}}{2}\)
- B \(1+\sqrt{2}\)
- C \(\frac{2 \sqrt{3}-1}{2}\)
- D \(\frac{3+\sqrt{3}}{2}\)
Answer & Solution
Correct Answer
(B) \(1+\sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(\cos A \cos B+\sin A \sin B \sin C=1 \Rightarrow (\cos A \cos B+\sin A \sin B) + \sin A \sin B (\sin C - 1)=1\) \(\Rightarrow \cos(A-B) + \sin A \sin B (\sin C - 1)=1\) Since \(\cos(A-B) \le 1\) and \(\sin A > 0, \sin B > 0, \sin C \le 1 \Rightarrow \sin C - 1 \le 0\), it must…
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