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Trigonometrical equations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTrigonometrical equations1 Mark
MCQ
The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is
  • ✓
    $\phi $
  • B
    $\{0\}$
  • C
    $\left\{ {\frac{\pi }{4}} \right\}$
  • D
    none of these
✓

Answer

Correct option: A.
$\phi $
a
$\tan (\pi \tan x)=\cot (\pi \cot x)$

$=\tan \left(\frac{\pi}{2}-\pi \cot x\right)$

$\Rightarrow \quad \pi \tan x=\frac{\pi}{2}-\pi \cot x$

$\Rightarrow \quad \tan x+\cot x=\frac{1}{2}$

$\Rightarrow \quad \tan x+\frac{1}{\tan x}=\frac{1}{2}$

$\Rightarrow \quad 2 \tan ^{2} x+2=\tan x$

$\Rightarrow \quad 2 \tan ^{2} x-\tan x+2=0$

This is quadratic in $\tan \mathrm{x}$.

$\Rightarrow \quad \tan x=\frac{1 \pm \sqrt{1-4.4}}{4}=\frac{1 \pm \sqrt{-15}}{2}$

which are not real

$\therefore $ solution set $=\phi$

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