Question

\[cos3x - cosx + sin4x =0\]
Find general solutions.

Answer 1

sin4x = sin2(2x)

Answer 2

=2 sin2x cos2x

Answer 3

let me try by this...

Answer 4

looks like your way would work; but it might get ugly..

Answer 5

http://www.wolframalpha.com/input/?i=cos+3x+%2B+sin+4x+%3D+cos+x

Answer 6

i prefer not using wolfram

Answer 7

use \[\cos p-\cos q\] identity for \[\cos 3x-\cos x\]

Answer 8

a substitution?

Answer 9

nope

\[\cos p-\cos q=-2 \sin \frac{p+q}{2}\sin \frac{p-q}{2}\]

Answer 10

is that a trig identity?

Answer 11

yeah...

Answer 12

well havent seen that identity before..i dont think it is needed..

Answer 13

thats a very important identity...try to keep it in your mind

\[\cos(A+B)=\cos A \cos B-\sin A \sin B\]\[\cos(A-B)=\cos A \cos B+\sin A \sin B\]subtract them \[\cos(A+B)-\cos(A-B)=-2\sin A \sin B\] let \(A+B=p\) and \(A-B=q\) to get that identity

Answer 14

ohh..i never knew that you can manipulate the compound-angle formula..
thanks; i will try it.

Answer 15

:)