- Home
- Standard 11
- Mathematics
8. Sequences and Series
hard
$( - \pi ,\,\,\pi )\,\,$ આંતરલમાં સમીકરણ $\,{{\rm{(8)}}^{{\rm{(1}}\, + \,{\rm{|cosx|}}\, + \,|{\rm{co}}{{\rm{s}}^{\rm{2}}}{\rm{x| }} + {\rm{ |co}}{{\rm{s}}^{\rm{3}}}{\rm{x|}}\, + ......{\rm{)}}}}\,\, = \,\,{4^3}$ નો ઉકેલ ક્યો છે ?
A
$ \pm \,\frac{\pi }{3},\, \pm \,\frac{\pi }{6}$
B
$ \pm \frac{\pi }{3},\, \pm \,\pi $
C
$ \pm \frac{\pi }{3},\, \pm \,\frac{{2\pi }}{3}$
D
આપેલ પૈકી એક પણ નહિ
Solution
$8^{\frac{1}{{{{1\, – \,|\cos \,x|}}}}}\,\, = \,\,{8^2}$
$\frac{1}{{1\,\, – \,\,|\cos \,x|}}\,\, = \,\,2\,$
$ \Rightarrow \,\,1\,\, – \,\,|\,\cos \,x|\,\, = \,\,\frac{1}{2}$
$|\cos \,x|\,\, = \,\,\frac{1}{2}\,\,\,$
$ \Rightarrow \,\,\,\cos \,x\,\, = \,\, \pm \,\,\frac{1}{2}$
$\left\{ { \pm \,\frac{\pi }{3}\,,\,\, \pm \,\frac{{2\pi }}{3}} \right\}\,$
Standard 11
Mathematics
