# Is it true $\int_0^{2\pi} \cos(k \theta) \cos(j \theta) d \theta = 0$ if $j \neq k$ and $j, k \geq 1$ are integers.

I am trying to check if this assertion is true, though i am bit rusty with integration and little unsure how to solve this integral.

Is the following statement true: $\int_0^{2\pi} \cos(k \theta) \cos(j \theta) d \theta = 0$ if $j \neq k$ and $j, k \geq 1$ are integers.

Any pointers of hints would be much appreciated.

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yes I have some familiarity with them, although no where near as much as i should. I have n't been lucky enough to study complex analysis yet. So have never undertaken complex variable integration. Hopefully one day soon. If you could give me a hint on what approach to use to solve the integral i'll be greatfull. –  Hardy Feb 19 '12 at 22:23
In general, the product of two $\sin,\cos$ or a $\sin$ and a $\cos$ may be converted to a sum, using the product to sum trigonometric identities. –  Américo Tavares Feb 19 '12 at 22:50

If you don't want to use complex detours, you can use the product formula for $\cos$:
$$\cos a \cos b = \frac12 (\cos(a+b) + \cos(a-b))$$