Final answer:
The trigonometric equation tan²(x) - 1 = 0 yields angles where tan(x) = ± 1, such as 45 or 225 degrees. The quadratic equation can be solved using the quadratic formula by identifying values of a, b, and c.
Step-by-step explanation:
The question posed involves solving a trigonometric equation and a quadratic equation. The trigonometric equation given is tan²(x) - 1 = 0, which can be solved by taking the square root of both sides, giving us tan(x) = ± 1. This means that the angle x could be 45 degrees (or π/4 radians) or 225 degrees (or 5π/4 radians) in the context of the unit circle, where the tangent function has the value of ± 1.
Moving on to the quadratic equation, it is given in the form x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0. This can be rearranged to match the standard quadratic equation format ax² + bx + c = 0, allowing us to use the quadratic formula. The solutions to the quadratic equation can be found by substituting the values of a, b, and c into the quadratic formula: x = (-b ± √(b² - 4ac))/(2a).