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Question Number 108114 by mathdave last updated on 14/Aug/20

Answered by mr W last updated on 14/Aug/20

$$\sin ({\sin }^{-1}\frac{4}{5}-{\cos }^{-1}\frac{4+3\sqrt{3}}{10})$$$$=\frac{4}{5}\times \frac{4+3\sqrt{3}}{10}-\frac{3}{5}\times \frac{4\sqrt{3}-3}{10}$$$$=\frac{1}{2}$$$$\Rightarrow {\sin }^{-1}\frac{4}{5}-{\cos }^{-1}\frac{4+3\sqrt{3}}{10}=\frac{\pi }{6}$$

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