Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Show that:

cos 20 degree space cos 40 degree space cos 60 degree space cos 80 degree space equals space 1 over 16

Answer
cos 20 degree space cos 40 degree space cos 60 degree space cos 80 degree space equals space cos 60 degree left square bracket cos 20 degree space cos 40 degree space cos 80 degree right square bracket
                           space space equals 1 half left square bracket cosA space cos left parenthesis 60 degree minus straight A right parenthesis space cos left parenthesis 60 degree plus straight A right parenthesis right square bracket space where space straight A space equals space 20 degree    
                             equals 1 half cross times space 1 fourth cos 3 straight A open square brackets because space cosA space cos left parenthesis 60 degree minus straight A right parenthesis space cos left parenthesis 60 degree plus straight A right parenthesis space equals space 1 fourth cos 3 straight A close square brackets
                              equals 1 over 8 cos left parenthesis 3 cross times 20 degree right parenthesis space equals space 1 over 8 space cos space 60 degree space equals space 1 over 8 cross times 1 half space equals space 1 over 16
Hence,      space space space cos 20 degree space cos 40 degree space cos 60 degree space cos 80 degree space equals space 1 over 16
                          

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