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3.Trigonometrical Ratios, Functions and Identities
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यदि $A + B + C = \pi ,$ तो ${\tan ^2}\frac{A}{2} + {\tan ^2}\frac{B}{2} + $${\tan ^2}\frac{C}{2}$ हमेशा है
A
$ \le 1$
B
$ \ge 1$
C
$= 0$
D
$= 1$
Solution
(b) $\tan \left( {\frac{A}{2} + \frac{B}{2} + \frac{C}{2}} \right) $
$= \frac{{{S_1} – {S_3}}}{{1 – {S_2}}} = \tan \frac{\pi }{2} = \infty $
$\therefore {S_2} = 1$ or $xy + yz + zx = 1$,
यहाँ $x = \tan \frac{A}{2}$ इत्यादि.
अब ${(x – y)^2} + {(y – z)^2} + {(z – x)^2} \ge 0$
या $2\sum {x^2} – 2\sum xy \ge 0 \Rightarrow \sum {x^2} \ge 1$. $\{ \because \sum xy = 1\} $
Standard 11
Mathematics
