Answer:
[tex]\sin ^2x-sinx\; cosx-sinx\; cosx+^{}\cos ^2x[/tex]
Explanation:
To prove the identity:
[tex](\sin x-\cos x)^2=\sec ^2x-\tan ^2x-2\sin x\cos x[/tex]
We have:
[tex]\begin{aligned} & (\sin x-\cos x)^2 \\ & =\sin ^2x-sinxcosx-sinxcosx+^{}\cos ^2x \\ & =\sin ^2x+\cos ^2x-2\sin x\cos x \\ & =1-2\sin x\cos x \\ & =\sec ^2x-\tan ^2x-2\sin x\cos x\end{aligned}[/tex]
Therefore, the missing line is:
[tex]\sin ^2x-sinx\; cosx-sinx\; cosx+^{}\cos ^2x[/tex]
