Question

If tan x + cot x = 2, then tan²x + x + cot²x is equal to ______.

Options

• 0

• 1

• 2

• 4

Answer 1

If tan x + cot x = 2, then tan²x + x + cot²x is equal to 2.

Explanation:

Let t = tan x, so `cot x = 1/t`. 

From `t + 1/t = 2`

Multiply by t to get t² + 1 = 2t 

⇒ t² – 2t + 1 = 0

⇒ (t – 1)² = 0

So, t = 1. 

Thus tan²x + cot²x

= 1² + 1²

= 2