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If the middel term of (x+(1)/(x)sinx)^(1...

If the middel term of `(x+(1)/(x)sinx)^(12)` is `(6237)/(16)` then the value of `sin^(-1)(sinx) ` is (are)

A

`(-pi)/(4)`

B

`(-pi)/(3)`

C

`(pi)/(4)`

D

`(pi)/(3)`

Text Solution

Verified by Experts

BD
Middle term `=""^(12)C_(6)x^(6)((sinx)/(x))^(6)=(6237)/(16)`
`sin^(6)x=((sqrt(3))/(2))^(6)`
`sin x=pm(sqrt(3))/(2)implies sin^(-1) sinx= pm(pi)/(3)`
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