Question

Simplify cos[arccsc((2√3)/3)].

Answer 1

Answer:

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