Solve cot^2θ-csc^2θ=

$$\cot ^ { 2 } \theta - \csc ^ { 2 } \theta =$$

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).

$$\left(\cot(\theta )-\frac{1}{\sin(\theta )}\right)\left(\cot(\theta )+\frac{1}{\sin(\theta )}\right)$$

Consider \cot(\theta )-\frac{1}{\sin(\theta )}. Factor out \frac{1}{\sin(\theta )}.

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

Consider \cot(\theta )+\frac{1}{\sin(\theta )}. Factor out \frac{1}{\sin(\theta )}.

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

Rewrite the complete factored expression.

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

Evaluate

$$-1$$