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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 \(\cot A \cot B+\cot B \cot C+\cot A \cot C\) ?

  1. A \(\infty\)
  2. B 1
  3. C -1
  4. D 0
Verified Solution

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…