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3.Trigonometrical Ratios, Functions and Identities
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જો $A + B + C = {180^o},$ તો $\frac{{\sin 2A + \sin 2B + \sin 2C}}{{\cos A + \cos B + \cos C - 1}} = $
A
$8\,\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$
B
$8\cos \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$
C
$8\,\sin \frac{A}{2}\cos \frac{B}{2}\cos \frac{C}{2}$
D
$8\,\cos \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$
Solution
(b) Here ${D^r} = 4\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}$
and ${N^r} = 4\sin A\sin B\sin c$
$\therefore L.H.S. = \frac{{{N^r}}}{{{D^r}}}$
and $\sin A = 2\sin \frac{A}{2}\cos \frac{A}{2}$ .
Standard 11
Mathematics
