Let `f(x)=e^(cos^(-1){sin(x+pi/3)})dot` Then, `f((8pi)/9)=` `e^(5pi//18)` (b) `e^(13pi//18)` (c) `e^(-2pi//18)` (d) none of these

Explanation

We have given

`f(x)=e^(cos^(-1)sin(x+pi/3))`

Let

`mu=cos^(−1)(sin(x−pi/3))`

`mu=(pi)/2-sin^(-1)(sin((-2pi)/9)
)`

`=(pi)/2+(2pi)/9=(13pi)/(18)`

Then, `f((8pi)/9)=e^(13pi//18)`

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