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Trigonometrical Equations
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ચલ $x$ એ સમીકરણ $\left| {\sin \,x\,\cos \,x} \right| + \sqrt {2 + {{\tan }^2}\,x + {{\cot }^2}\,x} = \sqrt 3$ એ ક્યાં અંતરાલમાં આવે છે ?
A
$\left[ {0,\frac{\pi }{3}} \right]$
B
$\left( {\frac{\pi }{3},\frac{\pi }{2}} \right)$
C
$\left[ {\frac{{3\pi }}{4},\pi } \right)$
D
શક્ય નથી
Solution
$|\sin x \cos x|+|\tan x+\cot x|=\sqrt{3}$
or $|\sin x \cos x|+\frac{1}{|\sin x \cos x|}=\sqrt{3}$
But $|\sin x \cos x|+\frac{1}{|\sin x \cos x|} \geq 2$
Hence, no solution.
Standard 11
Mathematics
