How do you solve $cos (x + \frac{π}{3}) + cos (x - \frac{π}{3}) = 1$ $cos(x+pi/3)+cos(x-pi/3)=1$ ?

Question

9323 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-08-20T16:24:19

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

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 $2npi+ 0= 2npi, n=0, +-1, +-2, +-3, ...$ .

How do you solve cos(x+pi/3)+cos(x-pi/3)=1cos(x+π3)+cos(x−π3)=1cos(x+pi/3)+cos(x-pi/3)=1?