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in any triangle ABC , (a+b)^2sin^2c/2+(a-b)^2cos^2c/2=

Asked by nd films 6th October 2018, 6:48 PM
Answered by Expert
Answer:
begin mathsize 16px style open parentheses straight a plus straight b close parentheses squared sin squared open parentheses straight c over 2 close parentheses plus open parentheses straight a minus straight b close parentheses cos squared open parentheses straight c over 2 close parentheses
equals straight a squared sin squared open parentheses straight c over 2 close parentheses plus 2 ab sin squared open parentheses straight c over 2 close parentheses plus straight b squared sin squared open parentheses straight c over 2 close parentheses plus straight a squared cos squared open parentheses straight c over 2 close parentheses minus 2 ab cos squared open parentheses straight c over 2 close parentheses plus straight b squared cos squared open parentheses straight c over 2 close parentheses
equals straight a squared sin squared open parentheses straight c over 2 close parentheses plus straight a squared cos squared open parentheses straight c over 2 close parentheses plus straight b squared sin squared open parentheses straight c over 2 close parentheses plus straight b squared cos squared open parentheses straight c over 2 close parentheses plus 2 absin squared open parentheses straight c over 2 close parentheses minus 2 abcos squared open parentheses straight c over 2 close parentheses
equals straight a squared plus straight b squared minus 2 ab open parentheses cos squared open parentheses straight c over 2 close parentheses minus sin squared open parentheses straight c over 2 close parentheses close parentheses
equals straight a squared plus straight b squared minus 2 abcosC
equals straight c squared end style
Answered by Expert 8th October 2018, 12:12 PM
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