Question

Express the sum or difference as a product. sin 4x - sin 6x

A. 2 cos 4x cos 5x

B. 2 sin 5x cos x

C. -2 sin x cos 5x

D. -2 sin x

Answer 1

@jim_thompson5910 @radar @sami-21

Answer 2

@cwrw238

Answer 3

Use the identity

\[\Large \sin(A)-\sin(B) = 2\cos\left(\frac{A+B}{2}\right)\sin\left(\frac{A-B}{2}\right)\]

Answer 4

this is a sum-to-product identity you can find them here
http://www.sosmath.com/trig/Trig5/trig5/trig5.html

oh - jim s got it

Answer 5

I got 2 cos(5x) sin(-x) that not a choice @jim_thompson5910

Answer 6

we used to try remembering these by something like

'twice cos semi sum sine semi difference'

- never found that very helpful

Answer 7

sine is an odd function, which means sin(-x) = -sin(x)

Answer 8

ohh so C?

Answer 9

yes

Answer 10

thanks!

Answer 11

np

Answer 12

@cwrw238, thanks for the link.

Answer 13

thats ok