How do you evaluate #sec(sec^-1((2sqrt3)/3))# without a calculator?

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Answer 1 · 2016-09-22T05:40:29

#2sqrt 3/3#

Use #f f^(-1)(c)=c#, for any function f that is locally bijective (single-

valued either way), at x = c.

For that matter,

#sin sin(-1)(c)#

#=cos cos^-1)(c)#

#=tan tan^(-1)(c)#

#=csc csc^(-1)(c)#

#=sec sec^(-1)(c)#

#=cot cot^(-1)(c)#

#=ln e^c#

#=log_b b^c#

#=c#.

Here,

#sec sec^(-1)(2sqrt 3/3)=2 sqrt 3/3#.