Question

Simplify (1 - sin^2 θ) x sec^2 θ.

Solution

1. From sin^2 θ + cos^2 θ = 1, we get 1 - sin^2 θ = cos^2 θ.
2. Also, sec θ = 1 / cos θ, so sec^2 θ = 1 / cos^2 θ.
3. The expression = cos^2 θ x (1 / cos^2 θ) = 1.