Question

If A + B + C = π and sin C + sin A cos B = 0, then tan A . cot B is equal to ______.

Options

• 0

• `-1/2`

• 1

• – 1

Answer 1

If A + B + C = π and sin C + sin A cos B = 0, then tan A . cot B is equal to `underlinebb(-1/2)`.

Explanation:

A + B + C = π

`\implies` sin C + sin A cos B = 0

`\implies` sin[π – (A + B)] + sin A cos B = 0

`\implies` sin(A + B) + sin A cos B = 0

`\implies` sin A cos B + cos A sin B + sin A cos B = 0

`\implies` 2 sin A cos B + cos A sin B = 0

`\implies` 2 sin A cos B = – cos A sin B

`\implies` tan A cot B = `(-1)/2`