In a triangle ABC, show that : tan B+C/2 = cot A/2

Asked by indirasolanki5661.9sdatl | 13th Mar, 2021, 10:43: AM

Expert Answer:

begin mathsize 16px style We space know space that comma
In space triangle ABC comma space straight m angle straight A plus straight m angle straight B space plus straight m angle straight C space equals space 180 degree
rightwards double arrow space angle straight B space plus angle straight C space equals space 180 degree minus angle A
rightwards double arrow fraction numerator angle straight B space plus angle straight C over denominator 2 end fraction equals 90 degree minus fraction numerator angle straight A over denominator 2 end fraction
rightwards double arrow tan open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses equals tan space open parentheses 90 degree minus straight A over 2 close parentheses equals space cot open parentheses straight A over 2 close parentheses
rightwards double arrow tan open parentheses fraction numerator straight B plus straight C over denominator 2 end fraction close parentheses equals cot open parentheses straight A over 2 close parentheses end style

Answered by Yasmeen Khan | 14th Mar, 2021, 09:17: PM