Question

Help?
Rewrite with only sin x and cos x.
sin 3x - cos x

Answer 1

do you know how to write sin(a+b)

Answer 2

That's what I thought I would do, too, @d3v13 . But these are my choicdes:
A) 2 sin x - sin3x - cos x
B) 2 sin x cos2x + sin x - 2 sin3x - cos x
C) 2 sin3x cos4x + 1
D) 3 sin x cos x - sin3x - cos x

Did I just overlook it?
\[\sin 3x - \cos x\]

Answer 3

any of the choices are not written only in sinx and cosx

Answer 4

My bad..
A) 2 sin x - sin^3x - cos x
B) 2 sin x cos^2x + sin x - 2 sin^3x - cos x
C) 2 sin^3x cos^4x + 1
D) 3 sin x cos x - sin^3x - cos x

Answer 5

oh makes more sense now

Answer 6

Thought it would.. :)

Answer 7

sin3x=sin(2x+x)=sin2xcosx + cos2xsinx

Answer 8

=2sinxcos^2x + cos2xsinx

Answer 9

okay got it

Answer 10

=2sinx(1-sin^2x) + (1-2sin^2x)sinx
=3sinx-4sin^3x

Answer 11

hence we can use
sin3x=3sinx-4sin^3x

Answer 12

sin3x-cosx = 3sinx-4sin^3x-cosx
=(2sinx-2sin^3x) + (sinx-2sin^3x-cosx)

Answer 13

=[2sinx(1-sin^2x)] + (sinx-2sin^3x-cosx)

Answer 14

=2sinxcos^2x + sinx - 2sin^3x - cosx
answer is B

Answer 15

Thank you so much! God bless you! :D