Question

Rewrite with only sin x and cos x.

sin (3x) - cos (x)

Please guide me with showing work because the process of substituting is what I'm having difficulties with.

Answer 1

So do you have any idea how to start?

Answer 2

sin (2x + x) - cos x ?

Answer 3

The identity for Sin(3x) is sin(3x) = -sin^3(x) + 3cos^2(x)sin(x)

Answer 4

I'm lost?
These are the choices:

Answer 5

substitute the identity I gave you into the problem. This gives -sin3(x)+3cos2(x)sin(x)-cos(x). Rearrange for positive term convention. 3cos2(x)sin(x-sin3(x)-cos(x) is the answer

Answer 6

Don't see it in the answer choices...

Answer 7

you're right, but the other identity for sin(3x) is -4sin3(x)+3sin(x). That definitly isn't the route to an answer.

Answer 8

you need to start by rewriting sin(3x)

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

you now need sin(2x) = 2sin(x)cos(x)

and cos(2x) = sos^2(x) - sin^2(x) and substitute them

so you will have

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

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

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

I'll let you finish by collecting like terms...

Answer 9

Omg, I understood it...
Thank you so much! :)