Question

sec^4theta-tan^4/sec^2+tan^2theta=sec^2-tan^2theta

Answer 1

\[\frac{\sec^4\theta-\tan^4\theta}{\sec^2\theta+\tan^2\theta}=\sec^2\theta-\tan^2\theta\]
With the LHS, factor the numerator using the difference of squares formula:
\[\sec^4\theta-\tan^4\theta=\left(\sec^2\theta+\tan^2\theta\right)\left(\sec^2\theta-\tan^2\theta\right)\]
The next step should be quite obvious.