Question

Rewrite with only sin x and cos x

sin 3x + cos 3x

Answer 1

sin(3x) = sin(2x + x)

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

= [sin(x)cos(x) + sin(x)cos(x)]cos(x) + sin(x)[cos(x)cos(x) - sin(x)sin(x)]
------------------------------------------

cos(3x) = cos(2x+x)

= cos(2x)cos(x)-sin(2x)sin(x)

= [cos(x)cos(x)-sin(x)sin(x)]cos(x) - [sin(x)cos(x)+sin(x)cos(x)]sin(x)

Answer 2

sin(3x) + cos(3x) =

2 sin(x)cos^2(x) + cos^2(x)sin(x) - sin^3(x) + cos^3(x)
-sin^2(x) cos(x) - sin^2(x) cos(x) - sin^2(x) cos(x)

simplify as needed