Solve 2cos (x) - 4sin (x) = 3 [0,360]

2cos (x) - 4sin (x) = 3

use identity [cos (x) ]^2 + [ sin (x) ]^2 = 1 = > cos (x) = √[1 - (sin (x)) ^2]

2√[1 - (sin (x)) ^2] - 4 sin (x) = 3

2√[1 - (sin (x)) ^2] = 3 + 4 sin (x)

square both sides

4[1 - (sin (x)) ^2] = 9 + 24 sin (x) + 16 (sin (x)) ^2

expand, reagrup and add like terms

4 - 4[sin (x) ]^2 = 9 + 24sin (x) + 16sin^2 (x)

20[sin (x) ]^2 + 24sin (x) + 5 = 0

use quadratic formula and you get sin (x) = - 0.93166 and sin (x) = - 0.26834

Now use the inverse functions to find x:

arcsin (-0.93166) = 76.33 degrees

arcsin (-0.26834) = 17.30 degrees