Variable x satisfying equation left| {sin ,x,cos ,x} right| + √ {2 + {{tan }^2},x + {{cot }^

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Trigonometrical Equations

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The variable $x$ satisfying the equation $\left| {\sin \,x\,\cos \,x} \right| + \sqrt {2 + {{\tan }^2}\,x + {{\cot }^2}\,x} = \sqrt 3$ belongs to the interval

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

non-existent

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

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