In any triangle ABC , ^2 A 2 + ^2 B 2 + ^2 C 2 is equal to - Vidyadip

MCQ

In any triangle $ABC ,$ ${\sin ^2}\frac{A}{2} + {\sin ^2}\frac{B}{2} + {\sin ^2}\frac{C}{2}$ is equal to

A
$1 - 2\,\cos \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$
B
$1 - 2\,\sin \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$
✓
$1 - 2\,\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$
D
$1 - 2\,\cos \frac{A}{2}\cos \frac{B}{2}\sin \frac{C}{2}$

✓

Answer

Correct option: C.

$1 - 2\,\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$

c
(c) Trick: For $A = B = C = {60^o}$ only option $(c)$ satisfies the condition.

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