Solve sec^2θ-tan^2θ=

$$\sec ^ { 2 } \theta - \tan ^ { 2 } \theta =$$

Factor

$$1$$

Solution Steps

The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(\frac{1}{\cos(\theta )}-\tan(\theta )\right)\left(\frac{1}{\cos(\theta )}+\tan(\theta )\right)$$

Consider \frac{1}{\cos(\theta )}-\tan(\theta ). Factor out \frac{1}{\cos(\theta )}.

$$\frac{1-\sin(\theta )}{\cos(\theta )}$$

Consider \frac{1}{\cos(\theta )}+\tan(\theta ). Factor out \frac{1}{\cos(\theta )}.

$$\frac{1+\sin(\theta )}{\cos(\theta )}$$

Rewrite the complete factored expression.

$$\left(1-\sin(\theta )\right)\left(1+\sin(\theta )\right)\times \left(\frac{1}{\cos(\theta )}\right)^{2}$$

Evaluate

$$1$$