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Question
Show that `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2 = (5pi)/6`.
Solution
LHS = `cos^-1 sqrt3/2 + 2 sin^-1 sqrt3/2`
`= cos^-1 (cos pi/6) + 2sin^-1 (sin pi/3) .....[because cos pi/6 = sqrt3/2 = sin pi/3]`
`= pi/6 + 2(pi/3) .....[because sin^-1 (sin "x") = "x", cos^-1 (cos x) = "x"]`
`= pi/6 + (2pi)/3`
`= (5 pi)/6` = RHS.
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