Comment upon $\gamma$

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 $\gamma$ .

#Geometry

Easy Math Editor

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Comments

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

Aditya Narayan Sharma - 4 years, 1 month ago

but how is it possible

Biswajit Barik - 4 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comment upon \(\gamma\)

Comments