Question

The value of cot A cot B + cot B cot C + cot C cot A is ______.

Options

• 4

• 3

• 2

• 1

Answer 1

The value of cot A cot B + cot B cot C + cot C cot A is 1.

Explanation:

In ΔABC, A + B + C = π

∴ A + B = π – C

∴ tan(A + B) = tan(π – C)

∴ `(tan A + tan B)/(1 - tan A tan B)` = tan(π – C)

∴ tan A + tan B = – tan C + tan A tan B tan C

∴ tan A + tan B + tan C = tan A tan B tan C

∴ `1/cotA + 1/cotB + 1/cotC = 1/cotA . 1/cotB . 1/cotC`

∴ cot A cot B + cot B cot C + cot C cot A = 1