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

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

1 Answer
Jun 4, 2016

1/2.

Explanation:

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