Find the principal value of:
sin^-1(root3 - 1/ 2root2)
 

Dear student,

Kindly find the answer to your query:
$$\begin{gathered} \mathrm{y} = {\sin }^{-1}\left(\frac{\sqrt{3}-1}{2\sqrt{2}}\right) \\ \sin 15= \sin \left(60-45\right)= \sin 60\cos 45-\cos 60\sin 45= \frac{\sqrt{3}}{2}\times \frac{1}{\sqrt{2}}-\frac{1}{2\sqrt{2}} \\ =\frac{\sqrt{3}-1}{2\sqrt{2}} \\ \mathrm{So}, \mathrm{y}= {\sin }^{-1}\left(\sin {15}^0\right)= {\sin }^{-1}\left(\sin \frac{\mathrm{\pi }}{12}\right)=\frac{\mathrm{\pi }}{12} \end{gathered}$$

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