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Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions5 Marks
Question
Find the general solution for each of the following equations:
$\cos4\text{x}=\cos2\text{x}$
✓

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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