Question

If `cot A + 1/(cot A) = 2`, find the value of `(cot^2A + 1/(cot^2A))`.

Answer 1

Given: `cot A + 1/(cot A) = 2`.

Step-wise calculation:

1. Let x = cot A (x ≠ 0).

2. `x + 1/x = 2`. Multiply both sides by x: x² + 1 = 2x.

3. Rearrange: x² – 2x + 1 = 0

⇒ (x – 1)² = 0

⇒ x = 1

4. Now compute `cot^2A + 1/(cot^2A)`

= `x^2 + 1/x^2`

= 1² + 1²

= 1 + 1

= 2