Question

Prove tan(C+A) /2=cot B/2.if ABC are interior angles

Answer 1

Step-by-step explanation:

We know that, in any triangle:

A + B + C = 180°

Therefore,

A + C = 180° - B

Dividing throughout by 2, we find:

$\frac{A + C}{2} = \frac{180° - B}{2} \\ \frac{A + C}{2} = 90 \degree - \frac{B}{2} \\ applying \: tan \: both \: sides : \\ tan(\frac{A + C}{2}) = tan(90 \degree - \frac{B}{2}) \\ tan(\frac{C + A}{2}) = cot \frac{B}{2} \\ thus \: proved$

Answer 2

Answer:

Here, C + A = 180˚ – B

(C + A)/2 = 90˚ – B/2

• Taking tan on both sides, we get

↠ tan (C + A)/2 = tan(90˚ – B/2)

= cot B/2

Hence proved.