PROVE THIS STATEMENT
 
SIN^6 A+COS^6 A = 1-3COS^2A . SIN^2A

Asked by dalbirgolagarh | 13th Jul, 2016, 09:05: PM

Expert Answer:

begin mathsize 12px style space LHS space equals space sin to the power of 6 straight A space plus thin space cos to the power of 6 straight A space
space space space space space space space space space equals space left parenthesis sin squared straight A right parenthesis cubed space plus thin space left parenthesis cos squared straight A right parenthesis cubed
space space space space space space space space space equals space left parenthesis sin squared straight A space plus thin space cos squared straight A right parenthesis cubed space minus 3 sin squared straight A space cos squared straight A space left parenthesis sin squared straight A space thin space plus space cos squared straight A right parenthesis.... left square bracket SInce comma space left parenthesis straight a plus straight b right parenthesis cubed equals straight a cubed plus straight b cubed space plus space 3 ab space left parenthesis straight a space plus space straight b right parenthesis right square bracket
space space space space space space space space space equals left parenthesis 1 right parenthesis cubed space minus space 3 space sin squared straight A space cos squared straight A space left parenthesis 1 right parenthesis space..... space left square bracket Since comma space sin squared straight A space plus space cos squared straight A space equals space 1 right square bracket
space space space space space space space space space equals 1 space minus space 3 space sin squared straight A space cos squared straight A
space space space space space space space space space equals RHS
Hence space proved. end style

Answered by Rebecca Fernandes | 13th Jul, 2016, 10:52: PM

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