.
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, . . .
The plot below confirms these solutions.
Plots y = and y = 1