MCQ
જો $A + B + C = \pi ,$ તો ${\tan ^2}\frac{A}{2} + {\tan ^2}\frac{B}{2} + $${\tan ^2}\frac{C}{2}$ એ . . ..
- A$ \le 1$
- ✓$ \ge 1$
- C$0$
- D$1$
$= \frac{{{S_1} - {S_3}}}{{1 - {S_2}}} = \tan \frac{\pi }{2} = \infty $
$\therefore {S_2} = 1$ or $xy + yz + zx = 1$,
where $x = \tan \frac{A}{2}$etc.
Now ${(x - y)^2} + {(y - z)^2} + {(z - x)^2} \ge 0$
or $2\sum {x^2} - 2\sum xy \ge 0 \Rightarrow \sum {x^2} \ge 1$. $\{ \because \sum xy = 1\} $
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