Question

890949Here is the proof of (sin x - cos x)2 = sec? x - tan” x - 2sin x cos x.What is the missing line?80%(sin x - cos x)2s= sin? x + cos2x - 2sin x cos X= 1 - 2sin x cos Xes4096= sec? x-tanx - 2sin x cos x

Answer 1

`\sin ^2x-sinx\; cosx-sinx\; cosx+^{}\cos ^2x`

Step-by-step explanation:

To prove the identity:

`(\sin x-\cos x)^2=\sec ^2x-\tan ^2x-2\sin x\cos x`

We have:

`\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}`

Therefore, the missing line is:

`\sin ^2x-sinx\; cosx-sinx\; cosx+^{}\cos ^2x`