The value of t a n - 1 1 - sin ⁡ x + 1 + sin ⁡ x 1 - sin ⁡ x - 1 + sin ⁡ x ∀ x ∈ 0 , π 2 is equal to

Question

The value of t a n - 1 1 - sin ⁡ x + 1 + sin ⁡ x 1 - sin ⁡ x - 1 + sin ⁡ x ∀ x ∈ 0 , π 2 is equal to, x 2 - π 2, x 2 + π 2, x 2 - π, π 2 - x 2

MARKS App · Accepted Answer

t a n - 1 1 - sin ⁡ x + 1 + sin ⁡ x 1 - sin ⁡ x - 1 + sin ⁡ x = t a n - 1 1 - sin ⁡ x + 1 + sin ⁡ x 1 - sin ⁡ x - 1 + sin ⁡ x 1 - sin ⁡ x + 1 + sin ⁡ x 1 - sin ⁡ x + 1 + sin ⁡ x = t a n - 1 1 - sin ⁡ x + 1 + sin ⁡ x + 2 1 - s i n 2 x 1 - sin ⁡ x - 1 + sin ⁡ x = t a n - 1 2 1 + cos ⁡ x - 2 sin ⁡ x = t a n - 1 - 2 c o s 2 x 2 2 s i n x 2 c o s x 2 = t a n - 1 - c o t x 2 = t a n - 1 c o t π - x 2 = π 2 - c o t - 1 c o t π - x 2 = π 2 - π - x 2 = x 2 - π 2

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