MCQ
$tan^{-1}2x+tan^{-1}\left(\frac{1}{x+4}\right)=\frac{\pi}{2}$ નો ઉકેલગણ ............ છે.
- ✓$\left\{4\right\}$
- B$\phi$
- C$\left\{ -4 \right\}$
- D$\left\{ 4,-4 \right\}$
$tan^{-1} x + tan^{-1} \left(\frac{1}{x +4}\right)$
અહી, $tan^{-1}x + tan^{-1} y = \frac{\pi}{2}$ $xy = 1$ પરથી
$\therefore \ 2x \left(\frac{1}{x + 4}\right) = 1$
$\therefore \ 2x = x +4$
$\therefore \ x = 4$
ચકાસણી $x = 4$ માટે,
$= tan^{-1}8 + tan^{-1} \frac{1}{8}$
$= \frac{\pi}{2}$
ઉકેલગણ $= \left\{4\right\}$
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