Proof:

To prove that sin^2/cos^2 1 = tan^2/sin^2, we can use trigonometric identities and basic algebraic manipulations. Let's break down the proof into several steps:

Step 1: Rewrite the given equation using trigonometric identities.
The trigonometric identity that relates the sine and cosine functions is:
sin^2 θ + cos^2 θ = 1

Using this identity, we can rewrite the equation as:
(sin^2 θ / cos^2 θ) / (1 / sin^2 θ) = (tan^2 θ / sin^2 θ)

Step 2: Simplify the left-hand side (LHS) of the equation.
To simplify the LHS, we can divide the numerator and denominator of the fraction by cos^2 θ:
(sin^2 θ / cos^2 θ) / (1 / sin^2 θ) = (sin^2 θ / cos^2 θ) * (sin^2 θ / 1)

This simplifies to:
(sin^2 θ / cos^2 θ) / (1 / sin^2 θ) = sin^4 θ / cos^2 θ

Step 3: Simplify the right-hand side (RHS) of the equation.
To simplify the RHS, we can use the trigonometric identity for the tangent function:
tan θ = sin θ / cos θ

We can square both sides of this identity to get:
tan^2 θ = (sin θ / cos θ)^2

Simplifying further:
tan^2 θ = sin^2 θ / cos^2 θ

Step 4: Compare the simplified LHS and RHS of the equation.
Comparing the simplified LHS and RHS, we find that they are equal:
sin^4 θ / cos^2 θ = tan^2 θ / sin^2 θ

Therefore, we have proven that sin^2/cos^2 1 = tan^2/sin^2.

Conclusion:
By using trigonometric identities and algebraic manipulations, we have shown that the equation sin^2/cos^2 1 = tan^2/sin^2 is true. This proof demonstrates the relationship between different trigonometric functions and highlights their interconnectedness.

if any1 ans plzz...