Can the following equations hold? Why? (1) 2cosx = 3 (2) sin ^ 2x0.5

Can the following equations hold? Why? (1) 2cosx = 3 (2) sin ^ 2x0.5

Obviously, the first one is impossible. It should be between - 1 and + 1 of cosx, so the first one is not true, and the second one seems not to be written clearly

Can the following equation hold: 1,2cosx = 3,2.sin square x = 0.5

If 1 does not hold, the maximum value of cosx is 1, 2 holds, (SiNx) ^ 2 = 0.5, SiNx = ± √ 2 / 2, such as x = ± 45 degrees

Can the following equation hold? Why? It's better to explain it in detail. Sin & sup2; X = 0.5 2cosx = 3

sin²x=0.5
sinx=±√2/2
Compliance - 1

The equation sin ^ 2x + sin 2x-2cos ^ 2x = m holds for all x ∈ R, and the value range of M is obtained
Detailed process. Thank you

Sin2x + sin2x-2cos ^ 2x = mm = sin2x + sin2x + cos ^ 2x-3cos ^ 2x = sin2x + 1-3 / 2 * (cos2x + 1) = sin2x-3cos2x / 2-3 / 2 + 1 = sin2x-3 / 2cos2x-1 / 2 because √ [(1 ^ 2 + (3 / 2) ^ 2] = √ 13 / 2, so m = √ 13 / 2 * 1 / (√ 13 / 2) * sin2x - (3 / 2) / (√ 13 / 2) cos2x) - 1 / 2 makes 1 / (...)