Max . value of sin - 1 2x + cos - 1 2x = pi / 2 , only when , - 1 / 2 ≤ x ≤ 1 / 2.
Again , when x = - 1 / 2 ,
sec - 1 2x = pi
Hence , max . value of the whole thing - 3 p i / 2
Similarly for x = 1 / 2 , the min value is -- p i / 2 as then sec - 1 2x = 0 .
Hence , ans -- 2 pi