In ABCcos 2 A -2- a -cos 2 B -2- b -cos 2 C -2- cA- S2-2 a b cB- S2-a b cC- S2-3 a b cD- None of these

The correct option is B We have, cos^2A 2/a+cos^2B 2/b+cos^2C 2/c ={s(s a) bc/a}+ {s(s b) ca/b} + {s(s c) ab/c} =s(s a+s b+s c)/abc =s[3s (c+b+c)]/abc =s(3s 2 ...

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Standard XI

Mathematics

Harmonic Progression

In ABCcos 2 A...

Question

In $△ A B C \frac{c o s^{2} \frac{A}{2}}{a} + \frac{c o s^{2} \frac{B}{2}}{b} + \frac{c o s^{2} \frac{C}{2}}{c}$

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None of these

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Solution

The correct option is B

We have, $\frac{c o s^{2} \frac{A}{2}}{a} + \frac{c o s^{2} \frac{B}{2}}{b} + \frac{c o s^{2} \frac{C}{2}}{c}$
= ${\frac{\frac{s (s - a)}{b c}}{a}} + {\frac{\frac{s (s - b)}{c a}}{b}} + {\frac{\frac{s (s - c)}{a b}}{c}}$
= $\frac{s (s - a + s - b + s - c)}{a b c}$
= $\frac{s [3 s - (c + b + c)]}{a b c}$
= $\frac{s (3 s - 2 s)}{a b c} = \frac{s^{2}}{a b c}$

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In △ABCcos2A2a+cos2B2b+cos2C2c

The correct option is B We have, cos2A2a+cos2B2b+cos2C2c ={s(s−a)bca}+{s(s−b)cab}+{s(s−c)abc} =s(s−a+s−b+s−c)abc =s[3s−(c+b+c)]abc =s(3s−2s)abc=s2abc

In $△ A B C \frac{c o s^{2} \frac{A}{2}}{a} + \frac{c o s^{2} \frac{B}{2}}{b} + \frac{c o s^{2} \frac{C}{2}}{c}$