solve 3 sin2y=2 tany?

Question

pls show the steps

Answer 1

6 sin y cos y = 2 sin y / cos y
6 sin y cos ² y - 2 sin y = 0
( 2 sin y)(3 cos ² y - 1) = 0
sin y = 0 , cos y = ± (1 / √3)
y = 0°,180°,360° ,54.7° ,125.3°, 234.7°, 305.3°

Answer 2

3 sin 2y=2 tan y
6 sin y cos y = 2 sin y/ cos y
One case: sin y = 0, or y = k*pi, k = 0, +-1, +-2, +-3, ...
Other case: sin y <> 0, so we have cos^2 y = 1/3
or: cos y = +-sqrt(3)/3
This y is not a special angle. Thus we write:
y = k*pi +- cos^(-1) (sqrt(3)/3), k = 0, +-1, +-2, +-3, ...
The complete solutions are:
y = k*pi, k*pi +- cos^(-1) (sqrt(3)/3), with k = 0, +-1, +-2, +-3, ...

Answer 3

sin2y=2 siny cosy
tany=siny/cosy

3 sin2y=2 tany => 3(2 siny cosy) = 2(siny/cosy)
=>3cosy=1/cosy =>(cos)^2 y = 1/3 =>
cosy = +_sqrt(3)/3 => y=kPi+_ Pi/6

Answer 4

i forg0t how