Question

. If A + B + C = 180°. prove that
tan (B+C/2)=cot A/2​

Answer 1

A+B+C=180

B+C =180-A

B+C /2=90-A/2

Therefore tan (B+C/2)=cot A/2.

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Answer 2

Given,

A+B+C=180°

divide by 2 on both sides

A/2 + B/2 + C/2 = 180°/2

A/2 + B/2 + C/2 = 90°

B/2 + C/2 = 90° - A/2

now take tan on both sides..

tan(B/2+C/2)=tan(90-A/2)

tan(B/2+C/2)=cotA/2

Hence proved