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Properties of Argument

In Δ ABC, if ...

Question

In $Δ A B C,$ if $b + c = 3 a$ then $cot \frac{B}{2} cot \frac{C}{2} =$

A

1

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B

2

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C

3

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D

4

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Solution

The correct option is B $2$
Given: $b + c = 3 a$
$\Rightarrow a + b + c = 4 a \Rightarrow s = 2 a$
We know, $cot \frac{A}{2} = \frac{s (s - a)}{Δ}$
$\Rightarrow cot \frac{B}{2} cot \frac{C}{2} = \frac{s (s - b) s (s - c)}{Δ^{2}} = \frac{s}{s - a} = \frac{2 a}{a} = 2$

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Similar questions

Q. Statement 1: In a

Δ A B C

b + c = 3 a

cot \frac{B}{2} cot \frac{C}{2} = 2

Statement 2: In a

Δ A B C

\frac{b + c}{a} = \frac{m}{n} (m > n

m, n

cot \frac{B}{2} cot \frac{C}{2} = \frac{m + n}{m - n}

Δ A B C, i f cos \frac{A}{2} = \sqrt{\frac{b + c}{2 c}},

Δ A B C,

A, B

C, cos (\frac{B + 2 C + 3 A}{2}) + cos (\frac{A - B}{2}) =

[\to a \to b \to c] = - 2

[\to a + 2 \to b, \to b - 2 \to c, \to c + 3 \to a] =

△ A B C, 3 a = b + c

, then the value of

cot \frac{B}{2} cot \frac{C}{2}

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Properties of Argument

Standard XII Mathematics

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