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Trigonometrical Equations
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સમીકરણ $\cos x - x + \frac{1}{2} = 0$ નો એક ઉકેલ નીચેનામાંથી ............. ગણમાં આવેલ છે
A
$\left( {0,\frac{\pi }{2}} \right)$
B
$\left( { - \frac{\pi }{2},0} \right)$
C
$\left( { \frac{\pi }{2},\pi } \right)$
D
$\left( {\pi ,\frac{{3\pi }}{2}} \right)$
Solution
Let $\mathrm{f}(\mathrm{x})=\cos \mathrm{x}-\mathrm{x}+\frac{1}{2}$
${f(0)=1+\frac{1}{2}>0} $
${f\left(\frac{\pi}{2}\right)=0-\frac{\pi}{2}+\frac{1}{2}=\frac{1-\pi}{2}<0}$
Therefore, one root lies in the interval $\left(0, \frac{\pi}{2}\right)$.
Standard 11
Mathematics
