Let S be the set of all solutions of the equation cos - 1 2 x - 2 cos - 1 1 - x 2 = π , x ∈ - 1 2 , 1 2 . Then ∑ x ∈ S 2 sin - 1 x 2 - 1 is equal to

Question

Let S be the set of all solutions of the equation cos - 1 2 x - 2 cos - 1 1 - x 2 = π , x ∈ - 1 2 , 1 2 . Then ∑ x ∈ S 2 sin - 1 x 2 - 1 is equal to, 0, - 2 π 3, π - sin - 1 3 4, π - 2 sin - 1 3 4

MARKS App · Accepted Answer

Given equation is: cos - 1 2 x - 2 cos - 1 1 - x 2 = π , x ∈ - 1 2 , 1 2 It is possible if cos - 1 2 x = π ....(1) and 2 cos - 1 1 - x 2 = 0 ....(2) From equation (1), x = - 1 2 which is not satisfying equation (2). So, no such x exists.

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