Question

The value of $\frac{{\sin }^4\mathrm{\theta }-{\cos }^4\mathrm{\theta }}{{\sin }^2\mathrm{\theta }-{\cos }^2\mathrm{\theta }}$ is ____________.

Answer 1

$$\begin{gathered} \frac{{\sin }^4\theta -{\cos }^4\theta }{{\sin }^2\theta -{\cos }^2\theta } \\ =\frac{{\left({\sin }^2\theta \right)}^2-{\left({\cos }^2\theta \right)}^2}{{\sin }^2\theta -{\cos }^2\theta } \\ =\frac{\left({\sin }^2\theta -{\cos }^2\theta \right)\left({\sin }^2\theta +{\cos }^2\theta \right)}{{\sin }^2\theta -{\cos }^2\theta }\left[a^2-b^2=\left(a-b\right)\left(a+b\right)\right] \end{gathered}$$
$$\begin{gathered} ={\sin }^2\theta +{\cos }^2\theta \\ =1 \end{gathered}$$

The value of $\frac{{\sin }^4\mathrm{\theta }-{\cos }^4\mathrm{\theta }}{{\sin }^2\mathrm{\theta }-{\cos }^2\mathrm{\theta }}$ is ______1______.