MATHS F.4......THX!!!

15. tanx tan(x/2) = 1 , 0=<x<360
2tan^2 (x/2) / (1-tan^2 (x/2)) = 1
3tan^2 (x/2) = 1
tan (x/2) = ± 1/√3
x/2 = 30 or x/2 = 150
x=60 or x=300

16. 3-4sin^2(x+10)=0, 180=<x=<270
3/4 = sin^2(x+10)
sin(x+10) = ±√3/2
x+10 = 240
x= 230

17. sin^2 2x - 3cos^2 2x = 0, 0=<x=<360
tan^2 2x - 3 = 0
tan 2x = ±√3
2x = 60 or 2x = 120 or 2x = 240 or 2x = 300 or
2x = 420 or 2x = 480 or 2x = 600 or 2x = 660
x=30 or x=60 or x=120 or x=150 or x=210 or x=240 or x=300 or x=330

21.a
3sin^2 x + 4sin x cos x - 4 cos^2 x = 0
3tan^2 x + 4tan x -4 = 0
b.
3sin^2 x + 4sin x cos x - 4 cos^2 x = 0
3tan^2 x + 4tan x -4 = 0
(tan x +2)(3tan x -2)=0
tan x = -2 or tan x = 2/3
x = 296.57 or x= 116.57 or x = 33.69 or x = 213.69

13.
2cos x/3 = √2, 0=< x<360
cos x/3 = √2/2
x/3 = 45
x= 135