If the minimum distance of the point ( sec ⁡ α , cosec ⁡ α ) from the circle x 2 + y 2 = 3 can be expressed as a - b , where a , b ∈ N , then the value of b a is

Step-by-step solution

Since, sec 2 ⁡ α + cosec 2 ⁡ α - 3 = 1 + tan 2 ⁡ α + 1 + cot 2 ⁡ α - 3 = - 1 + tan ⁡ α - cot ⁡ α 2 + 2 = 1 + tan ⁡ α - cot ⁡ α 2 > 0 Hence, the point sec ⁡ α , cos ⁡ e c α lies outside the circle x 2 + y 2 - 3 = 0 Now, the minimum distance = sec ⁡ α - 0 2 + cosec ⁡ α - 0 2 - 3 = 4 + tan ⁡ α - cot ⁡ α 2 - 3 (Minimum is attained, when tan ⁡ α = cot &#