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Simplify cos[arccsc((2√3)/3)].

User Flafoux
by
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2 Answers

5 votes

Answer:

It is 1/2

Explanation:

User Szmoore
by
3.5k points
6 votes

Answer:

1/2

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

User James Orr
by
3.2k points