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If in a ∆ABC ,cotA/2+cotB/2+cotC/2=k cotA/2cotB/2 cotC/2, then find the value of k.

Asked by azizrajil03 28th February 2019, 3:54 PM
Answered by Expert
Answer:
begin mathsize 16px style In space straight a space triangle comma
straight A plus straight B plus straight C equals straight pi
straight A over 2 plus straight B over 2 equals straight pi over 2 minus straight C over 2
tan open parentheses straight A over 2 plus straight B over 2 close parentheses equals tan open parentheses straight pi over 2 minus straight C over 2 close parentheses
fraction numerator tan straight A over 2 plus tan straight B over 2 over denominator 1 minus tan straight A over 2 tan straight B over 2 end fraction equals cot straight C over 2
fraction numerator begin display style fraction numerator tan straight A over 2 plus tan straight B over 2 over denominator tan straight A over 2 tan straight B over 2 end fraction end style over denominator begin display style fraction numerator 1 minus tan straight A over 2 tan straight B over 2 over denominator tan straight A over 2 tan straight B over 2 end fraction end style end fraction equals cot straight C over 2
fraction numerator cot straight B over 2 plus cot straight A over 2 over denominator cot straight B over 2 cot straight A over 2 minus 1 end fraction equals cot straight C over 2
cot straight B over 2 plus cot straight A over 2 equals cot straight C over 2 open parentheses cot straight B over 2 cot straight A over 2 minus 1 close parentheses
cot straight B over 2 plus cot straight A over 2 equals cot straight C over 2 cot straight B over 2 cot straight A over 2 minus cot straight C over 2
cot straight B over 2 plus cot straight A over 2 plus cot straight C over 2 equals cot straight C over 2 cot straight B over 2 cot straight A over 2
Comparing space with space question space we space get space straight k equals 1 end style
Answered by Expert 28th February 2019, 4:42 PM
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