Answer:
x = 90° or π/2 radians
Explanation:
We are given
cos²(x) + sin(x) = 1 [1]
The following identity is true:
cos²(x) + sin²(x) = 1 [2]
Subtract [1] from [2]
cos²(x) + sin²(x) - (cos²(x) + sin(x)) = 1 - 1
cos²(x) + sin²(x) - cos²(x) - sin(x) = 0
==> sin²(x) - sin(x) = 0
==> sin²(x) = sin(x)
Divide both sides by sin(x) to get
sin²(x)/sin(x) = sin(x)/sin(x)
==> sin(x) = 1
x = sin⁻¹(1)
x = 90° or π/2 radians