Question

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))))))?

Answer 1

If 2`sqrt3/3` is in degrees, the answer os nearly 1.

Explanation:

Follow nesting from innermost ().
inverse csc (2`sqrt3/3`) = 2`sqrt3/3`
cos2`sqrt3/3` =sin (`pi/2-`2`sqrt3/3`)
inverse sin of sin. operation gives the operand `pi/2-`2`sqrt3/3`
tan (.`pi/2-`2`sqrt3/3`) = cot ( 2`sqrt3/3`)
inverse cot cot operation give the operand 2`sqrt3/3`.
So, the answer is cos (2`sqrt3/3`) = cos (1.1457 deg) = 0.9998, nearly.