Prove the following identity: `(1/(sec^2theta-cos^2theta)+1/(cos e c^2theta-sin^2theta))sin^2thetacos^2theta=(1-sin^2thetacos^2theta)/(2+sin^2thetacos^2theta)`

Explanation

To prove the identity

\[ \left( \frac{1}{\sec^2 \theta - \cos^2 \theta} + \frac{1}{\cos^2 \theta - \sin^2 \theta} \right) \sin^2 \theta \cos^2 \theta = \frac{1 - \sin^2 \theta \cos^2 \theta}{2 + \sin^2 \theta \cos^2 \theta} \]

we will start by simplifying the left-hand side.

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