Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS4 Marks
Question
Find the general solution for each of the following equations: $\cos4\text{x}=\cos2\text{x}$
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Answer
$\cos4\text{x}=\cos2\text{x}$ $\Rightarrow\cos4\text{x}-\cos2\text{x}=0$ $\Rightarrow-2\sin\Big(\frac{4\text{x}+2\text{x}}{2}\Big)\sin\Big(\frac{4\text{x}-2\text{x}}{2}\Big)=0$ $\Big[\therefore\cos\text{A}-\cos\text{B=}-2\sin\Big(\frac{\text{A}+\text{B}}{2}\Big)\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)\Big]$ $\Rightarrow\sin3\text{x}\sin\text{x}=0$ $\Rightarrow\sin3\text{x}=0$ or $\sin\text{x}=0$ $\therefore3\text{x}=\text{n}\pi$ or $\text{x}=\text{n}\pi,$ where $\text{n}\in\text{Z}$ $\Rightarrow\text{x}=\frac{\text{n}\pi}{3}$ or $\text{x}=\text{n}\pi,$ where $\text{n}\in\text{Z}$
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