How do you prove #sin (x + y + z) = sin x cos y cos z + cos x sin y cos z + cos x cos y sin z - sin x sin y sin z#?

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Answer 1 · 2016-05-13T20:18:28

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Use Formulas: #sin (A+B)=sinAcosB+cosAsinB#

#cos(A+B)=cosAcosB-sinAsinB#

#A=x+y, B=z#

Left Side:#=sin((x+y)+z)=sin (x+y)cosz+cos(x+y)sinz#

#=(sinxcosy+cosxsiny)cosz+(cosxcosy-sinxsiny)sinz#

#=sinxcosycosz+cosxsinycosz+cosxcosysinz-sinxsinysinz#

#=#Right Side