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Question: If \(\tan\frac{B - C}{2} = x\cot\frac{A}{2}\), then \(x\)equal to...

If tan⁡B−C2=xcot⁡A2\tan\frac{B - C}{2} = x\cot\frac{A}{2}, then xxequal to

A

c−ac+a\frac{c - a}{c + a}

B

a−ba+b\frac{a - b}{a + b}

C

b−cb+c\frac{b - c}{b + c}

D

None of these

Answer

b−cb+c\frac{b - c}{b + c}

Explanation

Solution

We know, tan⁡B−C2=b−cb+ccot⁡A2\tan\frac{B - C}{2} = \frac{b - c}{b + c}\cot\frac{A}{2} ⇒ x=b−cb+cx = \frac{b - c}{b + c}.