Question

Rewrite with only sin x and cos x.

sin 3x - cos x

Answer 1

sin 3x = ?

Answer 2

sin(x +2x)

Answer 3

Yes!

We know that sin(a + b) = cos a sin b + cos b sin a.

So now, what does sin(x +2x) equal to?

Answer 4

Also, note that sin(2x) = 2sin(x)cos(x) and cos(2x) = cos²(x) – sin²(x) = 1 – 2sin²(x) = 2cos²(x) – 1

You're welcome.

Answer 5

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

Answer 6

Yeah, now replace sin(2x) to 2sin(x)cos(x) and cos(2x) to cos²(x) – sin²(x) or whatever you like to. You're done.

Answer 7

so

sin(x)cos²(x)-sin²(x)+2sin(x)cos(x)cos(x)-cos(x)??

Answer 8

1) 2 sin x - sin3x - cos x

2) 2 sin x cos2x + sin x - 2 sin3x - cos x

3) 2 sin3x cos4x + 1

4) 3 sin x cos x - sin3x - cos x

These are my 4 options and i don't seem to get any of them

Answer 9

???

The question says you have to rewrite the expression with only sin x and cos x.

Answer 10

My bad its actually

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