In ABC, if sin^2A + ^2B = ^2C, then show that a^2 + b^2 = c^2 - Vidyadip

Question

In $\triangle ABC$, if $sin^2A + \sin^2B = \sin^2C$, then show that $a^2 + b^2 = c^2$

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Answer

In $\triangle ABC$ by sine rule, we have
$ \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}=k$
$\therefore \sin A=k a, \sin B=k b, \sin C=k c$
$\text { Now, } \sin ^2 A+\sin ^2 B=\sin ^2 C \quad \ldots . . .[\text { Given] }$
$\therefore k^2 a^2+k^2 b^2=k^2 c^2$
$\therefore a^2+b^2=c^2 $

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