Question

Rewrite with only sin x and cos x.

sin 3x - cos x

Answer 1

Consider that: \[
\sin(3x) =\sin(x+2x) = \sin(x+(x+x))
\]And that: \[
\sin(x+y) = \sin(x)\cos(y)+\sin(y)\cos(x)
\]

Answer 2

Also:\[
\cos(x+y) = \cos(x)\cos(y) -\sin(x)\sin(y)
\]

Answer 3

I believe i have to rewrite it using Sin(2x) = 2sin(x)cos(x)

This is what i have

Sin(3x)-cos(x)

Sin(x+2x) - cos(x)

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

sin(x)+2sin(x)Cos(x)-cos(x)

Answer 4

lost after that

Answer 5

You made a mistake: \[
\sin(x+2x) - \cos(x)
\neq
\sin(x)+2\sin(x)-\cos(x)
\]

Answer 6

You have to use: \[
\sin(x+y) = \sin(x)\cos(y)+\sin(y)\cos(x)
\]You should try letting \(y=2x\), and going from there.

Answer 7

would it be

Sin(x)cos(2x)+sin(2x)cos(x)-cos(x) ?

Answer 8

yes

Answer 9

Now you have to use it again.

Answer 10

This equation: \[
\sin(2x) = 2\sin(x)\cos(x)
\]Is really just letting \(y = x\) in this equation: \[
\sin(x+y) = \sin(x)\cos(y)+\sin(y)\cos(x)
\]Since: \[
\begin{split}
\sin(2x) = \sin(x+x) = \sin(x)\cos(x)+\sin(x)\cos(x) = 2\sin(x)\cos(x)
\end{split}
\]

Answer 11

So then i Have

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

Answer 12

You should be showing your work.

Answer 13

sin(x)(1-2sin^2(x))+sin(x)cos(x)+sin(x)cos(x)-cos(x) is where i got it from,

changed the cos(2x) to (1-2sin^2(x)) in the formula

Answer 14

or would it be
sin(x)cos(2x)+sin(2x)cos(x)-cos(x)

sin(x)cos(x)cos(x)-sin(x)sin(x)+sin(x)cos(x)+sin(x)cos(x)cos(x)-cos(x)???

Answer 15

these are my options

1) 2 sin x - sin^3(x) - cos x

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

3) 2 sin^3(x) cos^4(x) + 1

4) 3 sin x cos x - sin^3(x) - cos x