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ICSE Class 10 Answered

If cos(a-b)+cos(b-c)+cos (c-a)= -3?2 ; then prove that  cos a +cos b+cos c+sin a +sinb +sinc=0 
Asked by keshavendu35 | 17 Aug, 2018, 12:10: AM
answered-by-expert Expert Answer
begin mathsize 16px style cos left parenthesis straight a minus straight b right parenthesis plus cos left parenthesis straight b minus straight c right parenthesis plus cos left parenthesis straight c minus straight a right parenthesis equals fraction numerator negative 3 over denominator 2 end fraction 2 left parenthesis cosacosb plus sinasinb plus cosbcosc plus sinbsinc plus cosccosa plus sincsina right parenthesis equals negative 3 2 left parenthesis cosacosb plus sinasinb plus cosbcosc plus sinbsinc plus cosccosa plus sincsina right parenthesis equals negative left parenthesis 1 plus 1 plus 1 right parenthesis 2 cosacosb plus 2 sinasinb plus 2 cosbcosc plus 2 sinbsinc plus 2 cosccosa plus 2 sincsina equals negative left parenthesis sin squared straight a plus cos squared straight a right parenthesis minus left parenthesis sin squared straight b plus cos squared straight b right parenthesis minus left parenthesis sin squared straight c plus cos squared straight c right parenthesis cos squared straight a plus cos squared straight b plus cos squared straight c plus 2 cosacosb plus 2 cosbcosc plus 2 cosccosa plus left parenthesis sin squared straight a plus sin squared straight b plus sin squared straight c plus 2 sinasinb plus 2 sinbsinc plus 2 sincsina right parenthesis equals 0 left parenthesis cosa plus cosb plus cosc right parenthesis squared plus left parenthesis sina plus sinb plus sinc right parenthesis squared equals 0 cosa plus cosb plus cosc equals 0 comma space sina plus sinb plus sinc equals 0 space space space space space space space space space space space space space space space space space space space space left parenthesis straight x squared plus straight y squared equals 0 rightwards double arrow straight x equals 0 comma space straight y equals 0 right parenthesis cosa plus cosb plus cosc equals sina plus sinb plus sinc equals 0 end style
Answered by Sneha shidid | 17 Aug, 2018, 11:18: AM

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