Rewrite with only sin x and cos x.

sin 3x

2 sin x cos2x + cos x

2 sin x cos2x + sin3x

sin x cos2x - sin3x + cos3x

2 cos2x sin x + sin x - 2 sin3x

Question

Rewrite with only sin x and cos x. 

sin 3x

 2 sin x cos2x + cos x

 2 sin x cos2x + sin3x

 sin x cos2x - sin3x + cos3x

 2 cos2x sin x + sin x - 2 sin3x

bahrom7893 · Answer

Sin(3x) = Sin(2x+x)

jhannybean · Answer

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

bahrom7893 · Answer

Just use double/triple angle formulas, and you're good to go.

jhannybean · Answer

sin(2x) cos(x) + cos(2x) sin(x) 

sin(2x) = 2 sin(x) cos(x) 

cos(2x) = 1 - 2 sin^(2) (x)

jhannybean · Answer

So... simplify 

sin(2x) cos(x) + cos(2x) sin(x) 

$\large \left(2sin(x)cos(x)\right)\left(cos(x)\right) + \left(1-2sin^{2}(x)\right)\left(sin(x)\right)$

jhannybean · Answer

Now simplify this and you'll get your answer :)

anonymous · Answer

so the last one?

jhannybean · Answer

$\large \left(2sin(x)cos^2(x)\right) + \left(sin(x)-2sin^3(x)\right)$

jhannybean · Answer

Yesss :D