SOLUTION: Find the general solution √3cosx+sinx=1

 = .

Multiply both sides by . You will get

 = .           (1)

Notice that  = ,  = . 

Substitute it into the left side of (1). You will get

 = .    (2)

Apply the formula sin(a)*cos(b) + cos(a)*sin(b) = sin(a+b) to the left side of (2). You ill get

 = .                       (3)

It implies 

 = ,  k = 0, +/-1, +/-2, . . . or

 = ,  k = 0, +/-1, +/-2, . . .


Thus there are two sets of solutions:

1.  x =  = ,  which is equivalent to  x = ,


and the other family


2.  x =  = 


Answer.  There are two sets of solutions:  1)  x =   and  2)  x = ,  k = 0, +/-1, +/-2, . . .