Question

If cos A = cos B cos C and A + B + C = π, then the value of cot B cot C is ______.

Options

• 1

• 2

• `1/3`

• `1/2`

Answer 1

If cos A = cos B cos C and A + B + C = π, then the value of cot B cot C is `underlinebb(1/2)`.

Explanation:

We have, cos A = cos B cos C

By triangle property, A + B + C = π

`\implies` B + C = π – A

∴ cos(B + C) = cos(π – A)

`\implies` cos(B + C) = – cos A

`\implies` cos B cos C – sin B sin C = – cos B cos C  ...[∵ given, cos A = cos B cos C]

`\implies` 2 cos B cos C = sin B sin C

`\implies (cos B cos C)/(sin B sin C) = 1/2`

`\implies` cot B cot C = `1/2`