Question

Solve sin(7x)cos(x) + cos(7x)sin(x) = sin(4x)

Answer 1

From 0 to 2pi

Answer 2

LOL nice profile picture and name

Answer 3

Haha thanks

Answer 4

try sum and difference identities?

Answer 5

Maybe, but I'm not supposed to know that for this course. Any other ideas?

Answer 6

what course is that?

Answer 7

Extension 1 Maths - Nsw Aus

Answer 8

subtract sin 4x from both sides and graph it

Answer 9

Graph it? Nah that would be cheating

Answer 10

graph it and sum/difference identities are the only ways I can think of to solve it

Answer 11

I'll give sum/difference a try

Answer 12

Yah on the left side we can see the `Angle Sum Identity for Sine` expanded out.
So if we work it backwards, we might be able to get where we need to go.

We currently have something like this:

\(\large \sin a\cos b+\sin b\cos a\) which will simplify down to \(\large \sin(a+b)\)

Answer 13

Of course! Thanks

Answer 14

Yeah that's done it

Answer 15

yep, that's a sum identity as I said before. Thank you zepdrix