Let \(\alpha,\beta\) and \(\gamma\) be the angles of a triangle with \(\alpha, \beta \in \left(0,\frac{\pi}{2}\right) \) satisfying \(\sin^{2} \alpha+\sin^{2} \beta=\sin \gamma\), what can you say about \(\gamma\)?

Rather, if you can then find the range of \(\gamma\).

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## Comments

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TopNewestbut how is it possible

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Did you try to simplify it to obtain \(\displaystyle \tan\left(\dfrac{\gamma}{2}\right)=\cos(\alpha-\beta)\) ?

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