Question

If A, B, C are the angles of AABC, then cot A. cot B + cot B. cot C + cot C. cot A =

• A. 0
• B. 1
• C. 2
• D. -1

Answer 1

Answer: (B)

1

Answer 2

For any triangle, the angles satisfy

$$A+B+C=\pi.$$

A well-known trigonometric identity for a triangle is

$$\cot A+\cot B+\cot C=\cot A\,\cot B\,\cot C.$$

Using this identity and appropriate trigonometric manipulations (which are standard in JEE/NEET problems), one can derive that

$$\cot A\cot B+\cot B\cot C+\cot C\cot A=1.$$