Moderate -0.3 This is a straightforward trigonometric equation requiring the compound angle formula for sin(x+45°), basic algebraic manipulation, and solving a linear trigonometric equation. The 'show that' part guides students through the key step, making it slightly easier than average. The solution involves standard techniques with no novel insight required.
Given the equation \(\sin(x + 45°) = 2\cos x\), show that \(\sin x + \cos x = 2\sqrt{2}\cos x\).
Hence solve, correct to 2 decimal places, the equation for \(0° < x < 360°\). [6]
Given the equation $\sin(x + 45°) = 2\cos x$, show that $\sin x + \cos x = 2\sqrt{2}\cos x$.
Hence solve, correct to 2 decimal places, the equation for $0° < x < 360°$. [6]
\hfill \mbox{\textit{OCR MEI C4 2012 Q5 [6]}}