Inverse function

yes i have got the ans = 2pi.
bcz It is a objective question..
with 4 ans and 2pi is one of them.
so can u show ur procedure.........

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