trignometry help!?

Question

solve the equation:

3 cosec x + 8 cos x = 0

for x the interval is 0< x < 180

please could you briefly tell wats goin on each step..thnxs!

Answer 1

3 cosec x + 8 cos x = 0
3 / sin x + 8 cos x = 0
3 + 24 sin x cos x = 0 . . . multiply both sides by sin x
2 sin x cos x = 3/12 = 1/4
sin 2x = 0.25
2x = 14.4775°
x = 7.2388°