Answer
$$\tan^2\theta(1+\cot^2\theta)=\frac{1}{\cos^2\theta}$$
Work Step by Step
$$A=\tan^2\theta(1+\cot^2\theta)$$
- For $\tan^2\theta$, we apply the identity $$\tan\theta=\frac{\sin\theta}{\cos\theta}$$
- For $1+\cot^2\theta$, we can use the identity $$1+\cot^2\theta=\csc^2\theta$$
However, we also have $\csc\theta=\frac{1}{\sin\theta}$. As such,
$$1+\cot^2\theta=\frac{1}{\sin^2\theta}$$
Replace all back to $A$:
$$A=\frac{\sin^2\theta}{\cos^2\theta}\times\frac{1}{\sin^2\theta}$$
$$A=\frac{1}{\cos^2\theta}$$
This is the result needed to find.
