Question
Solve the following equations:
$\cos\text{x}+\sin\text{x}=\cos2\text{x}+\sin2\text{x}$
$\cos\text{x}+\sin\text{x}=\cos2\text{x}+\sin2\text{x}$
$\Rightarrow\cos2\text{x}-\cos\text{x}+\sin2\text{x}-\sin\text{x}=0$
$\Rightarrow-2\sin\frac{3\text{x}}{2}\sin\frac{x}{2}+2\cos\frac{3\text{x}}{2}\sin\frac{\text{x}}{2}=0$
$\Rightarrow2\sin\frac{\pi}{\text{x}}\Big(\cos\frac{3\pi}{2}-\sin\frac{3\pi}{2}\Big)=0$
$\Rightarrow2\sin\frac{\text{x}}{2}=0$ or $\cos\frac{3\text{x}}{2}-\sin\frac{3\text{x}}{2}=0$
$\Rightarrow\sin\frac{\text{x}}{2}=0$ or $\cos\frac{3\text{x}}{2}=\sin\frac{3\text{x}}{2}$
$\Rightarrow\frac{\text{x}}{2}=\text{n}\pi$ or $\tan\frac{3\text{x}}{2}=1$
$\Rightarrow\text{x}=2\text{n}\pi$ or $\tan\frac{3\text{x}}{2}=\tan\frac{\pi}{4}$
$\Rightarrow\text{x}=\text{n}\pi$ or $\frac{3\pi}{2}-\text{n}\pi+\frac{\pi}{4}$
$\Rightarrow\text{x}=2\text{n}\pi$ or $3\text{x}=2\text{n}\pi+\frac{\pi}{2}$
$\Rightarrow\text{x}=2\text{n}\pi$ or $\text{x}=\frac{2\text{n}\pi}{3}+\frac{\pi}{6},\text{n}\in\text{Z}$
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| | Firm A | Firm B |
| No. of wage earners | 586 | 648 |
| Average weekly wages | 52.5 | 47.5 |
| Variance of the | 100 | 121 |
| Distribution of wages | | |
$\frac{\text{4x}+5\sin\text{x}}{\text{3x}+7\cos\text{x}}$
Length of major axis 16 foci
$(0, \pm6)$