Question

How do you solve `cos(x+pi/3)+cos(x-pi/3)=1`?

Answer 1

`x=2npi, n=0, +-1, +-2, +-3, ...`

Explanation:

Using `cos( A + B ) + co s( A - B ) = 2 cos A cos B`,

`2 cos x cos (pi/3)=1`.

As `cos(pi/3)=1/2`,

cos x = 1 = cos 0. Here 0 is the principal value `in [0. pi]`.

The general solution is `2npi+ 0= 2npi, n=0, +-1, +-2, +-3, ...`.