Question

Rewrite with only sin x and cos x.

sin 2x - cos 2x

Answer 1

This is so confusing because I know that what I did was correct, but my answer is not one of the choices.

Answer 2

well what do you know about

sin(2x)

and

cos(2x)

Answer 3

So I kind of made the choices as the guide, so here's what I did.

Answer 4

\[\sin2x-\cos2x\]
\[2 \sin x \cos x-(1-2\sin^2x)\]
\[2 \sin x \cos x -1+2\sin^2x\]

Answer 5

Here are the choices btw.

a.2 sinx cosx - 1 + 2 sin2x
b. 2 sin x cos2x - 1 + 2 sin2x
c. 2 sin x cos2x - sin x + 1 - 2 sin2x
d. 2 sin x cos2x - 1 - 2 sin2x

And my answer is A.

Answer 6

that works....

so looking at the answer options they have used

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

so as you have posted

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

Answer 7

I know that sin^2x = 2 sin x cos x
cos 2x = 1-2sin^2x
= 2 cos^2x-1
=cos^2x-sin^2x

Answer 8

you have the correct solution

Answer 9

So am I correct?

Answer 10

Oh okay thanks! :)

Answer 11

yes

\[2\sin(x)\cos(x) - 1 + 2 \sin^2(x)\]