Question

How do you solve for x given `cos 58=sqrt((1+cosx)/2)`?

Answer 1

`x = (720k+- 116)^o, k = 0, +-1, +-2, +-3...`.
In `(0, 360^o)`, ( for `k=0` and + sign) `x = 116^0 and 244^o` (equivalent to `-116^o`. for `k = 0` and negative sign )...

Explanation:

`sqrt((1+cosx)/2)=sqrt(cos^2(x/2)`

`=cos(x/2)=cos 58^o`

The general solution is

`x/2 = (360k+- 58)^o, k = 0, +-1, +-2, +-3...`. So,

`x = (720k+- 116)^o, k = 0, +-1, +-2, +-3...`.

In `(0, 360^o)`, ( for `k=0` and + sign) `x = 116^o and 244^o` (equivalent to `-116^o`, for `k = 0` and negative sign )...