In a triangle ABC - 2 b cos 2 C -2- c cos 2 B -2 is equal to -A- a-b-c B- a2-b2-c2C- a-b-cD- None of these

The correct option is A a + b + cWe know that cos(2θ cos^2 (θ ) 1 2 ( b cos^2C/2 +c cos^2B/2 ) = b 2. cos^2C/2 +c2. cos^2B/2 = b.( cos C+ 1 ) + c. (cos ...

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Standard XII

Mathematics

Projection Formula

In a triangle...

Question

In a triangle ABC , $2 (b c o s^{2} \frac{C}{2} + c c o s^{2} \frac{B}{2})$ is equal to -

a + b + c

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a^{2} + b^{2} + c^{2}

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a.b.c

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None of these

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Solution

The correct option is A a + b + c
We know that $c o s (2 θ c o s^{2} (θ) - 1$
$2 (b c o s^{2} \frac{C}{2} + c c o s^{2} \frac{B}{2})$
$= b 2. c o s^{2} \frac{C}{2} + c 2. c o s^{2} \frac{B}{2}$
$= b . (c o s C + 1) + c . (c o s B + 1)$
$= b . c o s C + c . c o s B + b + c$
From projection formula we know,
b.cos C + c. cos B = a
So, $2 (b c o s^{2} \frac{C}{2} + c c o s^{2} \frac{B}{2}) = a + b + c$

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