integration for :
cos(2x)*cos(3x)
please tell me the answer

Question

anonymous · Answer

I hope it is from -pi to pi

anonymous · Answer

no its indefinite integration

jamesj · Answer

$$ \cos 2x . \cos 3x = 1/2 ( \cos 5x + \cos x ) $$
Now just integrate that.

anonymous · Answer

why its not = 1/2(cos 5x - cos x )

anonymous · Answer

use double and triple angel identity

jamesj · Answer

cos(x+y) = cos x . cos y - sin x . sin y
cos(x-y) = cos x . cos y + sin x . sin y

hence

cos(x+y) + cos(x-y) = 2 cos x . cos y

$$ \implies \cos x . \cos y = \frac{1}{2} ( cos(x+y) + cos(x-y) ) $$

Thus

$$ \cos 2x . \cos 3x = \frac{1}{2} ( \cos 5x + \cos x ) $$

(remember cos(-x) = cos(x) )

anonymous · Answer

yes i noticed that cos(-x) = cos (x)
so cos(-x) will be cos (x)
thank you very much james

anonymous · Answer

ok tell me sin (-x) = ?
               tan (-x) = ?
               cot (-x) = ?
               sec (-x) = ?
               csc (-x) = ?

anonymous · Answer

sin (-x) aslo = sin (X)
?!

jamesj · Answer

sin(-x) = -sin(x).  And as you already know cos(x) = cos(-x).

From those two identities alone, you can derive all the others you are asking.

anonymous · Answer

aha thank you very much for your helping and caring

anonymous · Answer

james are u there ??