Simplify sine squared theta divided by the quantity 1 minus sine squared theta.

Solution:

The problem can be stated mathematically as:

sin²θ/(1 - sin²θ)

We know the fundamental trigonometric identity

sin²θ + cos²θ = 1

Therefore

(1 - sin²θ) = sin²θ + cos²θ - sin²θ = cos²θ

Therefore

sin²θ/(1 - sin²θ) = sin²θ/cos²θ = tan²θ

Simplify sine squared theta divided by the quantity 1 minus sine squared theta

Summary:

Simplifying sine squared theta divided by the quantity 1 minus sine squared theta we get tan²θ.