ત્રિકોણમિતીય પ્રતિવિધેયો — ગણિત ધોરણ 12 સાયન્સ — Question

$2tan^{-1} (cos x) = tan^{-1} (2 cosec x)$

$\therefore \ tan^{-1} (cos x) + tan^{-1} (cos x) = tan^{-1} (2 cosec x)$

$\therefore \ tan^{-1} \frac{cos x + cos x}{1 - cos x \ . \ cos x} = tan^{-1} \left(\frac{2}{sin x}\right) xy = cos x \ . \ cosx = cos^2x < 1$

$\therefore \ tan^{-1} \frac{2 cosx}{1 - cos^2x} = tan^{-1}\frac{2}{sin x}$

$\therefore \ \frac{2 cos x}{sin^2x} = \frac{2}{sin x}$

$\therefore \ \frac{cos x}{sin x} = 1$

$\therefore \ cot x = 1$

$\therefore \ cot x = cot \frac{\pi}{4}$

$\therefore \ x = \frac{\pi}{4}$

ચકાસણી

$= 2tan^{-1} \left(cos \frac{\pi}{4}\right)$

$= 2tan^{-1} \left(\frac{1}{\sqrt{2}}\right)$

$= tan^{-1} \frac{1}{\sqrt{2}} + tan^{-1} \frac{1}{\sqrt{2}}$

અહીંથી સ્વ-પ્રયત્નથી ગણવો.

ઉકેલગણ $= \left\{\frac{\pi}{4}\right\}$