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Question Number 100133 by bemath last updated on 25/Jun/20

$$\mathrm{If}{\sin }^{-1}\theta +{\sin }^{-1}\beta =\pi$$$$\theta +\beta -\frac{2}{{\theta }^2+{\beta }^2}=?$$

Answered by smridha last updated on 25/Jun/20

$${\sin }^{-1}\left(\mathit{\theta }\right)=\frac{\pi }{2}+\frac{\pi }{2}-{\sin }^{-1}\left(\mathit{\beta }\right)$$$${\sin }^{-1}\left(\mathit{\theta }\right)=\frac{\mathit{\pi }}{2}+{\cos }^{-1}\left(\mathit{\beta }\right)$$$$\mathit{\theta }=\mathit{s}\mathit{i}\mathit{n}(\frac{\mathit{\pi }}{2}+{\cos }^{-1}\left(\mathit{\beta }\right))=\mathit{c}\mathit{o}\mathit{s}\left({\cos }^{-1}\left(\mathit{\beta }\right)\right)$$$$\mathit{s}\mathit{o}\mathit{\theta }=\beta$$$$\mathit{n}\mathit{o}\mathit{w}\mathit{\theta }+\beta -\frac{2}{{\mathit{\theta }}^2+{\beta }^2}=2\mathit{\theta }-\frac{1}{2{\theta }^2}$$$$\mathit{o}\mathit{r}2\mathit{\beta }-\frac{1}{2{\mathit{\beta }}^2}.$$

Commented by bemath last updated on 25/Jun/20

$$\mathrm{thank}\mathrm{you}\mathrm{Mister}$$

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