Trigonometry Identities help?

Question

4sin^2 x +2cos^2 x=3

Sinx=cos 2x

Answer 1

4sin^2 x +2cos^2 x=3
4sin^2x +2(1-sin^2x) =3
4sin^2x +2 -2sin^2x =3
2sin^2x +2 = 3
sin^2 x =1/2
sinx x = +/-sqrt(1/2)
x = arcsin(sqrt(1/2)) = 45 or 135 degrees

Sinx=cos 2x
sinx = 1-2sin^2x
2sin^2x +sinx -1 = 0
(2sinx-1)(sinx +1) = 0
sin x= .5 or -1
x = 45 or 270 degrees

These were equations, not identities.

Answer 2

4 sin^2 x + 2 cos^2 x = 3

4sin^2 x + 2(1 - sin^2 x) = 3

4sin^2x + 2 - 2sin^2x = 3

2sin^2x - 1 = 0

2sin^2x = 1

sin^2x = 1/2

sinx =1/ sqrt(2)

x = pi/4

2)
sin x = cos 2x

sinx - (1-2sin^2x) = 0

sinx - 1 + 2sin^2x = 0

2sin^2x + sin x - 1 = 0

2sin^2x + 2sinx - sinx - 1 =0

2sinx(sinx +1) - 1(sinx + 1) = 0

(sinx + 1)(2sinx - 1) = 0

sinx = -1

x = 3pi/2

2sinx = 1

sinx = 1/2

= pi/6