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Question
Evaluate:
`tan^(-1) [2sin(2cos^(-1) (sqrt3)/2)]`
Evaluate
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Solution
Given: `tan^(-1) [2sin(2cos^(-1) (sqrt3)/2)]`
= `tan^(-1) [2sin(2 ⋅ pi/6)] ...[∵ (cos^(-1) (sqrt3)/2) = pi/6]`
= `tan^(-1) [2sin pi/3]`
= `tan^(-1) [2 xx (sqrt3)/2] ...(∵ sin pi/3 = (sqrt3)/2)`
= `tan^(-1) (sqrt3)`
= `pi/3`
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