Find the value of cos(inverse cot(tan(inverse sin(cos(inverse csc( 2radical3/3))))))?

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find the value of cos(inverse cot(tan(inverse sin(cos(inverse csc( 2radical3/3))))))?

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Answer 1 · 2016-06-04T07:26:46

#1/2#.

Let us work, starting from the innermost brackets.

#csc^(-1)(2sqrt 3/3)=csc^(-1)(2/sqrt 3)=sin^(-1)(sqrt 3/2)=pi/3#.

#cos(pi/3)=1/2#

#sin^(-1)(1/2)=pi/6#

#tan (pi/6) =1/sqrt 3#

#cot^(-1)(1/sqrt 3)=pi/2-pi/6=pi/3#.

Finally, the answer is #cos( pi/3)=1/2#