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Asked by sourabh7jain 16th June 2016, 5:32 PM
Answered by Expert
Answer:
open vertical bar table row cell negative 1 end cell cosC cosB row cosC cell negative 1 end cell cosA row cosB cosA cell negative 1 end cell end table close vertical bar
equals space minus 1 left parenthesis 1 space minus space cos squared straight A right parenthesis minus cosC left parenthesis negative cosC minus cosAcosB right parenthesis space plus space cosB space left parenthesis cosAcosC minus cosB right parenthesis
equals negative 1 space plus space cos squared straight A space plus space space cos squared straight C plus cosA space cosB space cosC plus cosA space cosB space cosC plus cos squared straight B
equals space cos squared straight A space plus space cos squared straight B space plus space space cos squared straight C space plus space 2 cosA space cosB space cosC space minus space 1
equals space cos squared straight A space plus space cos squared straight B space plus space space cosC space left square bracket cosC space plus space 2 space cosA space cosB right square bracket space minus space 1
Now comma space straight A space plus space straight B space plus space straight C space equals space straight pi space rightwards double arrow space straight A space plus space straight B space equals straight pi space minus space straight C
rightwards double arrow cos space left parenthesis straight A space plus space straight B right parenthesis space equals cos left parenthesis straight pi space minus space straight C right parenthesis
rightwards double arrow cos space left parenthesis straight A space plus space straight B right parenthesis space equals negative space cos space straight C... left parenthesis straight i right parenthesis
So comma space cos squared straight A space plus space cos squared straight B space plus space space cosC space left square bracket cosC space plus space 2 space cosA space cosB right square bracket space minus space 1
equals space cos squared straight A space plus space cos squared straight B space minus cos space left parenthesis straight A space plus space straight B right parenthesis left square bracket negative cos space left parenthesis straight A space plus space straight B right parenthesis space plus space 2 space cosA space cosB right square bracket space minus space 1.... left parenthesis from space left parenthesis straight i right parenthesis right parenthesis
equals cos squared straight A space plus space cos squared straight B space minus cos space left parenthesis straight A space plus space straight B right parenthesis left square bracket negative cos space left parenthesis straight A space plus space straight B right parenthesis space plus space cos left parenthesis straight A plus straight B right parenthesis plus cos left parenthesis straight A minus straight B right parenthesis right square bracket space minus space 1
space space space space space space space space space space space space space space space space space space space space space..... space left parenthesis Since space 2 space cosAcosB space equals space cos left parenthesis straight A plus straight B right parenthesis plus cos left parenthesis straight A minus straight B right parenthesis right square bracket
equals cos squared straight A space plus space cos squared straight B space minus cos space left parenthesis straight A space plus space straight B right parenthesis cos left parenthesis straight A minus straight B right parenthesis space minus space 1
equals cos squared straight A space plus space cos squared straight B space minus left square bracket cos squared straight A space minus sin squared straight B right square bracket space minus space 1
space space space space space space space space space space space space space space space space space space space space space..... space left parenthesis Since space cos space left parenthesis straight A plus straight B right parenthesis cos left parenthesis straight A minus straight B right parenthesis equals cos squared straight A space minus sin squared straight B right square bracket
equals cos squared straight A space plus space cos squared straight B space minus cos squared straight A space plus sin squared straight B space minus space 1
equals 1 space minus 1
equals 0
Answered by Expert 17th June 2016, 11:47 AM
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