Find the principal values of each of the following: (i) `"c o s e c"^(-1)(2/(sqrt(3)))` (ii) `"c o s e c"^(-1)(2cos(2/3pi))`

Explanation

(i) `cosec^(-1)(2/(sqrt(3)))`

`cosec y=2/(sqrt3)`

`cosec y=cosec(pi/3)`

The set of values of `cosec^(-1)(2/(sqrt(3)))` is `pi/3`


(ii) `"c o s e c"^(-1)(2cos((2pi)/(3))`

`=cosec^(-1)(-2cos((pi)/3))`

`=cosec^(-1)(-2 xx 1/2)`
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