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BabyGirl0419 BabyGirl0419
  • 11-04-2014
  • Mathematics
Answered

prove the identity

cos(A+B+C)=cosAcosBcosC-cosAsinBsinC-sinAcosBcosC-sinAsinBcosC

Verified Answer :

xxx102
xxx102 xxx102
  • 11-04-2014

Hello !

cos (a+b) = cos a cos b - sin a sin b
sin (a+b) = sin a cos b + sin b cos a

cos (a+b+c) = cos (a+(b+c))
cos (a+b+c) = cos a cos (b+c) - sin a sin (b+c)
cos (a+b+c) = cos a (cos b cos c - sin b sin c) - sin a (sin b cos c + sin c cos b)
cos (a+b+c)=cos a cos b cos c - cos a sin b sin c - sin a sin b cos c - sin a cos b sin c

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