Question

Rewrite with only sin x and cos x.

cos 3x

Answer 1

cos 3x is cos (2x + x) so you apply cos (A + B) and cos(2x) here

Answer 2

do you know what those are?

Answer 3

Yes those are familiar. cos a cos b + sin a sin b = something right?

Answer 4

wait it equals the cos(a+b) yeah

Answer 5

cos (A+B) is cosAcosB - sinAsinB

Answer 6

so cos(2x+x) = cos 2x cos x - sin 2x sin x
?

Answer 7

yes

Answer 8

then cos 2x is cos^2 x - sin^2 x

Answer 9

if you want to see why

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

thus cos^2 x - sin ^2 x

Answer 10

do you know the value of sin(2x)?

Answer 11

sin(2x) would be sinx sinx - cosx cosx
?

Answer 12

nope. sin(A+B) is sinAcosB + sinBcosA

so sin(2x) = sin(x+x) = sinxcosx + sinxcosx

Answer 13

that gives you 2sinxcosx

Answer 14

a)cos x - 4 cos x sin2x

b) -sin3x + 2 sin x cos x

c) -sin2x + 2 sin x cos x

d) 2 sin2x cos x - 2 sin x cos x

Those are the answers. I think all we need to do now is simplify

Answer 15

yes simplify everything