Solve for x.

Question

sqr(3)(sin(x))+(cos(x))=2

 

How do i get an answer of x = π/3 +2kπ, k=0,±1,±2,±3...(i.e.,...,-5π/3,π/3,7π/3,...)

 

The π is pi

Answer 1

divide both side equation by 2:

(sqr(3))/2*sinx + 1/2 * cosx = 1

 

since (sqr(3))/2 = sin(π/3) and 1/2 = cos(π/3)

 

rewrite the above equation:

 

sin(π/3) * sinx + cos(π/3) * cosx = cos (0 + k2π)

 

  =>   cos (x - π/3) = cos (0 + k2π)

  =>         (x - π/3) =   k2π

        =>             x =  π/3 +  k2π