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Trigonometrical Equations
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સમિકરણ $\frac{1}{2} +cosx + cos2x + cos3x + cos4x = 0$ નો ઉકેલ . . . . મેળવો.
A
$x=\frac{2n\pi}{9},n\in I,n\neq 9m,m\in I$
B
$x=\frac{2n\pi}{9},n\in I,n= 9m,m\in I$
C
$x=\frac{n\pi}{9}+\frac{\pi}{2},n\in I$
D
$x=\frac{2n\pi}{3}+\frac{\pi}{6},n\in I$
Solution
$\frac{1}{2}+\frac{1}{2 \sin \frac{x}{2}} 2 \sin \frac{x}{2}(\cos x+\cos 2 x+\cos 3 x+\cos 4 x)=0$
$=\frac{1}{2}+\frac{1}{2 \sin \frac{x}{2}}\left(\sin \frac{9 x}{2}-\sin \frac{x}{2}\right)=0$
$=\frac{\sin \left(\frac{9 \mathrm{x}}{2}\right)}{\sin \left(\frac{\mathrm{x}}{2}\right)}=0 $
$ \Rightarrow \mathrm{x}=\frac{2 \mathrm{n} \pi}{9}, \mathrm{n} \neq 9 \mathrm{mm} \in \mathrm{I}$
Standard 11
Mathematics
