Integration sines and cosines question

[ilikephysics]

Express the sines and cosines in exponential form and integrate to show that (integral from -pi to pi) sin(3x)cos(4x)dx=0

What I'm thinking is that I should use sin x=e^x-e^-x/2 and cos x=e^x+e^-x/2. And I should multiply sin times 3 and cos times 4 and integrate. And get something like this:

(e^3pi+e^-3pi/2 * e^4pi-e^-4pi/2) - (e^-3pi+e^3pi/2 * e^-4pi-e^4pi/2)=0

I don't think this is right though. Can someone help please?

 

[cookiemonster]

Try looking up and using some trig reduction formulas.

cookiemonster

 

[HallsofIvy]

Yes, I would be inclined to use "reduction formulas" but if the problem specifically said "Express the sines and cosines in exponential form", then the way ilikephysics is approaching this is correct.

However, the formulas are wrong!

$$sin(x)= \frac{e^{ix}-e^{-ix}}{2i}$$
$$cos(x)= \frac{e^{ix}+e^{-ix}}{2}$$

ilikephysics forgot the "i"s.