Question

cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x is equal to ______.

विकल्प

• – 1

• 0

• 1

• `1/2`

Answer 1

cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x is equal to 1.

Explanation:

We know that, cot 3x = cot(2x + x)

`\implies` cot 3x = `(cot 2x cot x - 1)/(cot 2x + cot x)`

`\implies` cot 3x . cot 2x + cot 3x . cot x = cot 2x . cot x – 1

`\implies` cot 3x . cot 2x + cot 3x . cot x – cot 2x . cot x = – 1

`\implies` cot x . cot 2x – cot 2x . cot 3x – cot 3x . cot x = 1