AP EAMCET · Maths · Trigonometric Ratios & Identities
In a \(\triangle A B C\), suppose none on the angles are multiples of \(\frac{\pi}{2}\), then what is the value \(\cot A \cot B+\cot B \cot C+\cot A \cot C\) ?
- A \(\infty\)
- B 1
- C -1
- D 0
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } A+B+C=\pi \text { and } A, B, C \neq \frac{n \pi}{2} \\ & \cot (B+C)=\frac{\cot B \cot C-1}{\cot B+\cot C} \\ & \Rightarrow \quad \cot (\pi-A)=\frac{\cot B \cdot \cot C-1}{\cot B+\cot C} \\ & \Rightarrow \quad-\cot A(\cot B+\cot C)=\cot B \cdot…
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