If the middle term of ` (x + 1/x"sin"^(-1)x)^(8) " is equal to (630)/(16)` ,
the value of x is/are

Options

A. `- (pi)/(3)`
B. `-(pi)/(6)`
C. `(pi)/(6)`
D. `(pi)/(3)`

Answer

a,d

Explanation

Here , n is even , so middle term is `((8)/(2) + 1)` th , i.e. 5th term
` therefore T_(5) = ""^(8)C_(4) (x)^(4) ((sin^(-1) x)/(x))^(4) = (630)/(16)` [given]
` rArr 70(sin^(-1) x)^(4) = (630)/(10) rArr (sin^(-1) x)^(4) = (9)/(16)`
` rArr (sin^(-1) x)^(2) = (3)/(4) rArr sin^(-1) x = pm (sqrt(3))/(2)`
` rArr x = - (pi)/(3) , (pi)/(3) [ because sin^(-1) x in (- (pi)/(2), (pi)/(2))]` .