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With usual notation prove that 2 ( a sin^2 C/2+c sin^2 A/2 ) = a + c- b

Asked by shahsamaira2 8th January 2018, 5:28 PM
Answered by Expert
Answer:
begin mathsize 16px style sin squared straight theta equals fraction numerator 1 minus cos 2 straight theta over denominator 2 end fraction
LHS
equals 2 open parentheses straight a space sin squared open parentheses straight C over 2 close parentheses plus straight c space sin squared open parentheses straight A over 2 close parentheses close parentheses
equals 2 open parentheses straight a fraction numerator 1 minus cos space straight C over denominator 2 end fraction plus straight c space fraction numerator 1 minus cos space straight A over denominator 2 end fraction close parentheses
equals straight a minus straight a space cos space straight C plus straight a minus straight c space cos space straight A
equals straight a plus straight c minus left parenthesis straight a space cos space straight C plus straight c space cos space straight A right parenthesis
equals straight a plus straight c minus straight b..... left parenthesis cosine space rule space right parenthesis end style
Answered by Expert 9th January 2018, 2:13 PM
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