Solve tan^2θ-sec^2θ=

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

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).

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

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

$$-1$$