- A student attempts to answer the following question:
Given that \(x\) is an obtuse angle, use algebra to prove by contradiction that
$$\sin x - \cos x \geqslant 1$$
The student starts the proof with:
Assume that \(\sin x - \cos x < 1\) when \(x\) is an obtuse angle
$$\begin{aligned}
& \Rightarrow ( \sin x - \cos x ) ^ { 2 } < 1
& \Rightarrow \ldots
\end{aligned}$$
The start of the student's proof is reprinted below.
Complete the proof.
Assume that \(\sin x - \cos x < 1\) when \(x\) is an obtuse angle
$$\Rightarrow ( \sin x - \cos x ) ^ { 2 } < 1$$