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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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    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](http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Product-to-sum_and_sum-to-product_identities) trigonometric identities.2012-02-19

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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)) $