| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 3 |
| Topic | Trig Proofs |
| Type | Prove trigonometric identity |
| Difficulty | Standard +0.3 This is a straightforward trigonometric identity proof requiring standard double angle formulas and compound angle expansion. Students need to expand the LHS using cos(A+B), apply double angle identities, and verify equivalence—routine techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.01a Proof: structure of mathematical proof and logical steps1.05l Double angle formulae: and compound angle formulae1.05p Proof involving trig: functions and identities |
Prove that $\sqrt{2}\cos(2\theta + 45°) \equiv \cos^2\theta - 2\sin\theta\cos\theta - \sin^2\theta$, where $\theta$ is measured in degrees. [3]
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q4 [3]}}