Moderate -0.3 This is a straightforward identity proof requiring application of the compound angle formula for sin(θ+45°) and cos(θ+45°), followed by recognition that the resulting expression matches the double angle formula -cos(2θ+90°) = sin(2θ). While it requires knowing multiple formulae, the algebraic manipulation is routine and the path is clear, making it slightly easier than average.
## Question 4:
Use of $\cos(A+B)$ or $\sin(A+B)$ or $\cos 2\theta$ formula | **M1** | AO 3.1a | Correct formula
Correct result | **A1** | AO 2.1 |
Use of one of the above or $\sin 2\theta$ formula | **M1** | AO 1.1 | Correct formula
Correctly obtain result | **A1** | AO 1.1 |
**Example of method:**
$\sin^2(\theta+45) - \cos^2(\theta+45) \equiv -\cos 2(\theta+45)$ | **M1** | | Use of correct $\cos 2\theta$ formula
| **A1** | | Correct result
$\equiv -\cos(2\theta+90)$ | **M1** | | Use of correct $\cos(A+B)$ formula
$\equiv -[\cos 2\theta\cos 90 - \sin 2\theta\sin 90] \equiv \sin 2\theta$ **AG** | **A1** [4] | | Must see this step and final answer
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