6 Solve the equation \(2 \cos 2 x = 1 + \cos x\), for \(0 ^ { \circ } \leqslant x < 360 ^ { \circ }\).
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Question 6:
Answer Marks
Guidance
Answer Marks
Guidance
\(2\cos 2x = 2(2\cos^2 x - 1) = 4\cos^2 x - 2\) M1
Any double angle formula used
\(\Rightarrow 4\cos^2 x - 2 = 1 + \cos x\) M1
Getting a quadratic in \(\cos x\)
\(\Rightarrow 4\cos^2 x - \cos x - 3 = 0\) M1dep
Attempt to solve
\(\Rightarrow (4\cos x + 3)(\cos x - 1) = 0\) A1
For \(-3/4\) and \(1\)
\(\Rightarrow \cos x = -3/4\) or \(1\) \(\Rightarrow x = 138.6°\) or \(221.4°\) or \(0\) B1 B1
139, 221 or better
B1 www
\(-1\) extra solutions in range
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## Question 6:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2\cos 2x = 2(2\cos^2 x - 1) = 4\cos^2 x - 2$ | M1 | Any double angle formula used |
| $\Rightarrow 4\cos^2 x - 2 = 1 + \cos x$ | M1 | Getting a quadratic in $\cos x$ |
| $\Rightarrow 4\cos^2 x - \cos x - 3 = 0$ | M1dep | Attempt to solve |
| $\Rightarrow (4\cos x + 3)(\cos x - 1) = 0$ | A1 | For $-3/4$ and $1$ |
| $\Rightarrow \cos x = -3/4$ or $1$ | | |
| $\Rightarrow x = 138.6°$ or $221.4°$ or $0$ | B1 B1 | 139, 221 or better |
| | B1 | www |
| | | $-1$ extra solutions in range |
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6 Solve the equation $2 \cos 2 x = 1 + \cos x$, for $0 ^ { \circ } \leqslant x < 360 ^ { \circ }$.
\hfill \mbox{\textit{OCR MEI C4 Q6 [7]}}