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Find the value of: `tan^(-1)[2cos(2sin^(-1)(1/2)]`

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Find the value of: `tan^(-1)[2cos(2sin^(-1)(1/2)]`
A. `(pi)/(4)`
B. `-(pi)/(4)`
C. `(3pi)/(4)`
D. `(3pi)/(4)`
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We know that `sin^(-1)1/2=(pi)/(6)`
`therefore tan^(-1){2cos(2sin^(-1)1/2)}`
`=tan^(-1)(2xx1/2)=tan^(-1)1=(pi)/(4)`
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