Solve sec^2t-tan^2t

$$\sec ^ { 2 } t - \tan ^ { 2 } t$$

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).

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

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

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

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

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

Rewrite the complete factored expression.

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

Evaluate

$$1$$