Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=0

Answer 1

sin^2x-3cosx+sinxcosx-3sinx=0
sin^2x - 3sinx + sinxcosx - 3cosx = 0
sinx(sinx - 3) + cosx(sinx - 3) = 0
(sinx - 3)(sinx + cosx) = 0
sinx = 3 , which is not possible
or
sinx = -cosx
sinx/cosx = -1
tanx = -1
x = 135° or 225° or in radians, 3π/4 , 5π/4
the period of tanx = 180° or π radians

general solution: = 3π/4 + kπ
or
x = 5π/4 + kπ , where k is an integer