- Home
- Standard 11
- Mathematics
Trigonometrical Equations
hard
સમીકરણ $\cos x - x + \frac{1}{2} = 0$ નું એક બીજ . . . . . અંતરાલમાં 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
(a) $f(x) = \cos x – x + \frac{1}{2}$,
$f(0) = \frac{3}{2} > 0$
$f\left( {\frac{\pi }{2}} \right) = 0 – \frac{\pi }{2} + \frac{1}{2} = \frac{{1 – \pi }}{2} < 0$,
$\left( \because {\;\pi = \frac{{22}}{7}{\rm{ nearly}}} \right)$
$\therefore$ One root lies in the interval $\left[ {0,\,\frac{\pi }{2}} \right]$.
Standard 11
Mathematics
