4sin (x)=3cos (×) =>cos (x)=?

4 sin(x) = 3 cos(x)
[4 sin(x)]² = [3 cos(x)]²
16 sin²(x) = 9 cos²(x)
16 [1 - cos²(x)] = 9 cos²(x)
16 - 16 cos²(x) = 9 cos²(x)
25 cos²(x) = 16
cos²(x) = 16/25
cos(x) = 4/5 or cos(x) = -4/5

4sin(x) = 3cos(x)
sin(x)/cos(x) = 3/4
tan(x) = 3/4
tan(x)^2 = 9/16
sec(x)^2 - 1 = 9/16
sec(x)^2 = 25/16
cos(x)^2 = 16/25
cos(x) = +/- 4/5

4 sin(x) = 3 cos(x)
divide both sides by cos(x)
4 sin(x) /cos(x) = 3
4 tan(x) = 3
tan(x) = 3/4
tan(x) = opp/adj (in a right triangle)
opp = 3
adj = 4
hyp = sqrt( 3^2+4^2) = sqrt(25)= 5 (Pythogorean Theorem)

cos(x) = adj/hyp = +/- 4/5

Ans:

tan x = 3 / 4

cos x = 4 / 5

sin x = 3 / 5