Question

If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = ______.

Options

• 0

• 1

• 2

• – 1

Answer 1

If A, B, C are the angles of ΔABC then cotA.cotB + cotB. cotC + cotC + cotA = 1.

Explanation:

We know that if A + B + C = π, then tan A + tan B + tan C = tan A tan B tan C

`\implies 1/(tanB tanC) + 1/(tanA tanC) + 1/(tanA tan B)` = 1

`\implies` cot B cot C + cot A cot C + cot A cot B = 1