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Provide Solution For R.D.Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Exercise Multiple Choice Questions Question 15 Maths Textbook Solution.

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Answer: e^{\frac{13 \pi}{18}}

Hint: Take cos function to the RHS, so the variables get free.

Given: e^{\cos ^{-1}}\left\{\sin \left(x+\frac{\pi}{3}\right)\right\}

We have to compute f\left(\frac{8 \pi}{9}\right)


\mathrm{f}(\mathrm{x})=e^{\cos ^{-1}}\left\{\sin \left(x+\frac{\pi}{3}\right)\right\}

f\left(\frac{8 \pi}{9}\right)=e^{\cos ^{-1}}\left\{\sin \left(\frac{8 \pi}{9}+\frac{\pi}{3}\right)\right\}

                  =e^{\cos ^{-1}}\left\{\sin \left(\frac{11 \pi}{9}\right)\right\}

                   =e^{\cos ^{-1}}\left\{\cos \left(\frac{\pi}{2}+\frac{13 \pi}{18}\right)\right\}

                   =e^{\cos ^{-1}}\left\{\cos \left(\frac{13 \pi}{18}\right)\right\}

          f\left(\frac{8 \pi}{9}\right)=e^{\frac{13 \pi}{18}}


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