Question

Find the value of cos9x × cos4x

Answer 1

Answer:

Most times with trigonometric functions, you'll have to apply trigonometric identities to make them work inside of an integral. In this case, we'll be using the trigonometric ID of:

cos(u)*cos(v) = (1/2)*[cos(u-v)+cos(v+u)]

This will give us all we need as we prepare to solve this problem.

Using 9x=u and 4x=v (or vice versa) we apply the ID to obtain the following integral:

∫ (1/2)*[cos(5x)+cos(13x)] dx

From there we can split up the integral into parts, or two separate integrals.

∫ (1/2)*cos(5x) dx + ∫ (1/2)*cos(13x) dx

Now we can do a simplified integral to find our solution (knowing already the integral of a cosine function). We now have our answer:

(1/10)*sin(5x) + (1/13)*sin(13x) + C

Step-by-step explanation:

hope this help you.