Question

If A + B = 45°, then (cot A – 1) (cot B – 1) is equal to ______.

Options

• 3

• `1/2`

• – 1

• 2

Answer 1

If A + B = 45°, then (cot A – 1) (cot B – 1) is equal to 2.

Explanation:

Given, A + B = 45°

cot (A + B) = 1

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

`\implies` cot A cot B – (cot A + cot B) = 1  ...(i)

Now, (cot A – 1) (cot B – 1)

= cot A cot B – (cot A + cot B) + 1

= 1 + 1  ...[From equation (i)]

= 2