Simplify cos[arccsc ((2√3) / 3) ].

1/2

Step-by-step explanation:

Given the expression cos[arccsc ((2√3) / 3) ]

let y = arccsc ((2√3) / 3)

Taking cosec of both sides we have;

cosecy = cosec[arccsc ((2√3) / 3) ]

cosecy = (2√3) / 3

1/siny = (2√3) / 3

sin y = 3/2√3

Rationalizing 3/2√3

= 3/2√3 * √3/√3

= 3√3/2*3

= 3√3/6

= √3/2

siny = √3/2

y = arcsin (√3/2)

y = 60°

Since y = arccsc ((2√3) / 3) = 60°

cos[ arccsc ((2√3) / 3) ] = cos60°

cos60° = 1/2