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
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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.