2sec²(x) - 2sec²(x)sin(x) - sin²(x) - cos²(x) = 1
2sec²(x) - 2sec²(x)sin(x) - sin²(x) - cos²(x) = sin²(x) + cos²(x)
+ sin²(x) + cos²(x) + sin²(x) + cos²(x)
2sec²(x) - 2sec²(x)sin(x) = 2sin²(x) + 2cos²(x)
2[sec²(x)] - 2[sec²(x)sin(x)] = 2[sin²(x) + cos²(x)]
2[sec²(x) - sec²(x)sin(x)] = 2(1)
2 2
sec²(x) - sec²(x)sin(x) = 1
sec²(x) sec²(x)
1 - sin(x) = cos²(x)
sin²(x) + cos²(x) - sin(x) = cos²(x)
- cos²(x) - cos²(x)
sin²(x) - sin(x) = 0
sin(x)[sin(x)] - sin(x)[1] = 0
sin(x)[sin(x) - 1] = 0
sin(x) = 0 or sin(x) - 1 = 0
sin⁻¹[sin(x)] = sin⁻¹(0) + 1 + 1
x = 0 sin(x) = 1
sin⁻¹[sin(x)] = sin⁻¹(1)
x ≈ 1.5707
The solution is actually equal to zero.
