sinθ / 1-cos^2 θ

Rewrite the expression as a single trigonometric ratio.

sinθ / 1-cos^2 θ

= sinθ /sin^2 θ
= 1/sin θ or csc θ, where sinθ ≠ 0

Thank you very much! :)

To rewrite the expression sinθ / 1 - cos^2 θ as a single trigonometric ratio, we need to simplify it using trigonometric identities.

First, let's recall the Pythagorean identity: sin^2 θ + cos^2 θ = 1.

We can rewrite the denominator of the expression using this Pythagorean identity:

1 - cos^2 θ = sin^2 θ

Now, substituting sin^2 θ for 1 - cos^2 θ in the original expression, we get:

sinθ / (sin^2 θ)

Next, we can rewrite this expression using the reciprocal identity: cscθ = 1 / sinθ.

Using the reciprocal identity, we can rewrite the expression as:

cscθ * sinθ

Now, we have rewritten the expression sinθ / 1 - cos^2 θ as a single trigonometric ratio, which is cscθ * sinθ.