1) sin^2(x) = 0,5
sin(x) = ±√0,5
sin(x) = ±0,7071
x = π/4 + 2πk, 3π/4 + 2πk, 5π/4 + 2πk, 7π/4 + 2πk, k ∈ Z

2) 2sin^2(x) + 3cos(x) - 3 = 0
2(1 - cos^2(x)) + 3cos(x) - 3 = 0
2 - 2cos^2(x) + 3cos(x) - 3 = 0
2cos^2(x) - 3cos(x) = -1
2cos^2(x) - 3cos(x) + 1 = 0
(cos(x) - 1)(2cos(x) - 1) = 0
cos(x) = 1 или cos(x) = 0,5
x = 0 + 2πk, k ∈ Z или x = π/3 + 2πk, 5π/3 + 2πk, k ∈ Z

3) sin^2(x) - 10sin(x)cos(x) + 21cos^2(x) = 0
sin^2(x) - 10sin(x)cos(x) + 21(1 - sin^2(x)) = 0
sin^2(x) - 10sin(x)cos(x) + 21 - 21sin^2(x) = 0
-20sin^2(x) + sin^2(x) - 10sin(x)cos(x) + 21 = 0
-19sin^2(x) - 10sin(x)cos(x) + 21 = 0
(19sin(x) - 3)(sin(x) + 7) = 0
sin(x) = 3/19 или sin(x) = -7
There are no real solutions for sin(x) = -7

4) cos^2(π-x) + 8cos(π+x) + 7 = 0
cos^2(π-x) = sin^2(x)
sin^2(x) + 8(-cos(x)) + 7 = 0
sin^2(x) - 8cos(x) + 7 = 0
sin(x) = 1 и cos(x) = 7
There are no real solutions for sin(x) = 1/7.