visa att (Har försökt skriva med formeleditorn)

Är lite frågande.$$\begin{gathered} \frac{1}{{\tan }^2\left(x\right)}- {\cos }^2\left(x\right)={\cos }^2· \frac{1}{{\displaystyle {\tan }^2}{\displaystyle (}{\displaystyle x}{\displaystyle )}} \\ ---------------- \\ VL \\ \frac{{\displaystyle 1}}{{\displaystyle {\tan }^2\left(x\right)}}- {\cos }^2\left(x\right) (vill få till samma nämnare) \\ \frac{{\displaystyle 1}}{{\displaystyle {\tan }^2\left(x\right)}} -\frac{{\displaystyle {\cos }^2}{\displaystyle ·}{\displaystyle {{\displaystyle \tan }}^2}{\displaystyle (}{\displaystyle x}{\displaystyle )}}{{\displaystyle {\tan }^2}{\displaystyle (}{\displaystyle x}{\displaystyle )}} (samma nämnare) \\ \frac{(1-{\cos }^2(x\left)\right){\tan }^2\left(x\right)}{{\displaystyle {\tan }^2}{\displaystyle (}{\displaystyle x}{\displaystyle )}}= \\ \frac{{\displaystyle (1-{\cos }^2(x\left)\right)·\frac{{\displaystyle {\sin }^2}{\displaystyle (}{\displaystyle x}{\displaystyle )}}{{\displaystyle {\cos }^2}{\displaystyle (}{\displaystyle x}{\displaystyle )}}}}{{\displaystyle {\tan }^2}{\displaystyle (}{\displaystyle x}{\displaystyle )}} (nu är jag frågande) \end{gathered}$$