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A,B and C are acute angles of triangle ABC. Prove tan(A+B)/2=cot C/2

Asked by subhasray1968 21st December 2017, 9:59 PM
Answered by Expert
Answer:
begin mathsize 16px style straight A plus straight B plus straight C equals 180 degree
straight A plus straight B equals 180 degree minus straight C
fraction numerator straight A plus straight B over denominator 2 end fraction equals fraction numerator 180 degree minus straight C over denominator 2 end fraction
tan open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses equals tan open parentheses 90 degree minus straight C over 2 close parentheses
tan open parentheses fraction numerator straight A plus straight B over denominator 2 end fraction close parentheses equals cot straight C over 2 end style
Answered by Expert 22nd December 2017, 8:53 AM
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