Would sin^2x / cos^2x equal tan^2x?
Yes, sin^2x / cos^2x is equal to tan^2x.
To understand why this is true, let's break it down step by step:
1. Start with the given expression: sin^2x / cos^2x.
2. Recall the trigonometric identity for tangent: tan(x) = sin(x) / cos(x). This identity comes from the definition of tangent as the ratio of sine to cosine.
3. Now, square both sides of the tangent identity: tan^2(x) = (sin(x) / cos(x))^2.
4. Simplify the right side of the equation: tan^2(x) = sin^2(x) / cos^2(x).
5. As you can see, the expression derived in step 4 is identical to the original expression sin^2x / cos^2x. Therefore, sin^2x / cos^2x and tan^2x are equal.
So, to answer your question, sin^2x / cos^2x does indeed equal tan^2x.