Standard +0.8 This is a proof by contradiction involving trigonometric inequalities, requiring students to assume the negation, manipulate the inequality algebraically (likely squaring both sides), and derive a contradiction using the Pythagorean identity. While the technique is standard A-level, the non-routine application to a trigonometric inequality and the need to carefully handle the domain restrictions makes this moderately challenging.
Prove by contradiction that, for every real number $x$ such that $0 \leqslant x \leqslant \frac{\pi}{2}$,
$$\sin x + \cos x \geqslant 1.$$ [4]
\hfill \mbox{\textit{WJEC Unit 3 2018 Q11 [4]}}