Question

rewrite with only sinx and cosx : sin 3x + cos3x

Answer 1

sin(2x +x)+cos(2x+x)

Answer 2

2sinxcosxcosx+2cos^2x-1cosx

Answer 3

sin(3x)= sin(x+2x)=sinxcos2x+cos2xsinx
cos(3x)=cos(x+3x)=cosxcos2x-sinxsin2x

Answer 4

sin2x=2sinxcosx
cos2x=cos^2x-sin^2x

Answer 5

\[sinx(\sin^2x-\cos^2x)+cosx(2sinxcosx)+cosx(\sin^2x-\cos^2x)-sinx(2sinxcosx)\]

Answer 6

The missing part is:
\[-sinx(2sinxcosx)\]

Answer 7

Simplifies to -sin^3x+cos^3x+3sinxcos^2-3sin^2xcosx