Question

Simplify the expression 125 − 5x2 as much as possible after substituting 5 sin(θ) for x. (Assume 0° < θ < 90°.)

Answer 1

125 - 5x² = 0  when x = 5 sin θ

⇒ 125 - 5(5 sinθ)²

⇒ 125 - 5(25 sin²θ)

⇒ 125 - 125 sin²θ

⇒ 125(1 - sin²θ)

⇒ 125(1 - sinθ)(1 + sinθ)          This is simplified

Solving for θ:

⇒ (1 - sinθ)(1 + sinθ) = 0          

⇒ (1 - sinθ) = 0        (1 + sinθ) = 0

⇒    sinθ = 0               sinθ = -1

        θ = 0°                  θ = 180°

Since neither value satisifies 0° < θ < 90°  there is no solution