For the principal values, evaluate the following: `sin^(-1)(-(sqrt(3))/2)+cos e c^(-1)(-2/(sqrt(3)))` `sec^(-1)(sqrt(2))+2cos e c^(-1)(-sqrt(2))` `sin^(-1)[cos{2cos e c^(-1)(-2)}]` `cos e c^(-1)(2tan(11pi)/6)`

Explanation

`sin^(-1)(-(sqrt(3))/2)=y`

`sin y= -(sqrt 3)/2`

`-sin y=(sqrt3)/2`

`-sin pi/3`

`-sin(pi/3)=sin(-pi/3)`

The range of principal value of `sin^(-1)` is `(-pi/2, pi/2)` and `sin(-pi/3)=-(sqrt3)/2`

`cosec^(-1)(-sqrt3/2)=z`

`-cosec z= sqrt3/2`
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