How do you evaluate $sec^-1(2/sqrt3)$ without a calculator?

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Answer 1 · 2016-12-01T16:02:17

$sec^(-1)(2/sqrt(3)) = pi/6$

Find $x$ such that $sec x = 2/sqrt(3)$

As:

$secx = 1/cosx$

this is the same as finding $x$ such that $cos x =sqrt(3)/2$ and we know that:

$cos(pi/6) = sqrt(3)/2$

How do you evaluate sec^-1(2/sqrt3)sec^-1(2/sqrt3) without a calculator?