Question

Rewrite with only sin x and cos x. sin 2x - cos 2x

Answer 1

I know to use the identities, but I am having issues simplifying for my answer choices. I have 2sinx cosx -1-2sin^2x

Answer 2

for one
sin(2x) - cos(2x) ==> 2sin(x)cos(x) -[ 1-sin\(^2\)( x)]

Answer 3

so, that leaves you with
2sin(x)cos(x) -1+sin\(2\)( x)

Answer 4

why is the - distributed?

Answer 5

because is in FRONT of the function

Answer 6

Oh ok that makes sense, that is where I went wrong thanks.

Answer 7

\(-1+2sin^2(x)\) I mean, kinda missed the "2" there

Answer 8

$$
2sin(x)cos(x)-1+2sin^2(x) \implies
2sin(x)\pmatrix{cos(x)+sin(x)}-1
$$

Answer 9

I had just messed up the sign for the last sin, thanks so much for your help