"simplify cos(x-30)-cos(x+30)"

[MrMath]

How should I approach the following problem:
"simplify cos(x-30)-cos(x+30)"

Thanks!

 

[ksdhart2]

One way to go is to use the angle sum and difference identities. If you're having trouble finding these in your class notes and/or textbook, you might try this page. Using those, the problem turns into [cos(x) cos(30) + sin(x) sin(30)] - [cos(x) cos(30) - sin(x) sin(30)]. Can you finish up from here?

 

[MrMath]

Thank you!

One way to go is to use the angle sum and difference identities. If you're having trouble finding these in your class notes and/or textbook, you might try this page. Using those, the problem turns into [cos(x) cos(30) + sin(x) sin(30)] - [cos(x) cos(30) - sin(x) sin(30)]. Can you finish up from here?

Thank you so much for your assistance, now I understand!

 

[tkhunny]

Another way is simply to add them. There are ways...

\(\displaystyle \cos(x-30^{\circ}) - \cos(x+30^{\circ}) = \cos(x-90^{\circ}) = \sin(x)\)