Insanely easy question - trig functions, need a quick question answered

[andrew.c]

Homework Statement

I need to solve the equation $$cos 5x + cos 3x = cos x$$

Do the first two terms add together to be cos 8x? Then use double angle formula to solve?

 

[rl.bhat]

Homework Statement

I need to solve the equation $$cos 5x + cos 3x = cos x$$

Do the first two terms add together to be cos 8x? Then use double angle formula to solve?

No. cos 5x + cos 3x is not equal to cos8x.
Use formula to convert sum of trig. function to product form.

 

[Architeuthis Dux]

Thank you for your question. Yes, you are correct in thinking that the first two terms can be combined to become cos 8x. However, instead of using the double angle formula, you can use the sum-to-product identity for cosine to rewrite the equation as 2cos 4x cos x = cos x. From here, you can divide both sides by cos x and solve for cos 4x, and then use the inverse cosine function to find the value of x. I hope this helps!