trig problem, i need help please!!!!

Question

Let x = 4 sin 𝜃, − 𝜋/2 < 𝜃 < 𝜋/2.

 Simplify the expression.

x/16-x^2 

Answer 1

If x = 4sinθ, then x / √(16 - x²) = 4sinθ / √(16 - 16sin²θ) = 4sinθ / [√16(1 - sin²θ)] = 4sinθ / [4√(1 - sin²θ)] =

sinθ / √cos²θ = sinθ / cosθ = tanθ