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
A. S. Adikesavan
Mar 7, 2016

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.

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