Question

Here is proof of (sin x - cos x)^2 = sec^2x- tan^2x - 2sin x cos x What is the MISSING line?

Answer 1

1st option:

`\sin ^2x-2\sin x\cos x+\cos ^2x`

Explanation:

We have the following expression:

`\mleft(\sin x-\cos x\mright)^2`

In this case, the square of the subtraction is applied as if it were two algebraic terms, like this:

`\begin{gathered} (a-b)^2=a^2-2ab+b^2 \\ \text{ in this case} \\ (\sin x\: -\: \cos \: x)^2=\sin ^2x-2\cdot\sin x\cdot\cos x+\cos ^2x \end{gathered}`

Which means the answer is:

`\sin ^2x-2\sin x\cos x+\cos ^2x`