3sin(x) + 4cos(x) = 5  ---> 


 = 1.


Let "a" be the angle in QI such that cos(a) = ,  sin(a) = .

Such an angle does exists since  = 1.


Then 

1 =  = cos(a)*sin(x) + sin(a)*cos(x) = sin(a+x) = sin(x+a).

It implies that x + a =  and, hence, x = ,  where a =