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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 | 28 Feb, 2019, 03:54: PM
answered-by-expert 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 Sneha shidid | 28 Feb, 2019, 04:42: PM
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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 | 28 Feb, 2019, 03:54: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
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