MCQ
$\left(\frac{sin \theta}{sin \phi}\right)^2 =\frac{tan \theta}{tan \phi} = 3 $ હોય, તો ......... .
- ✓$tan \phi = \frac{1}{\sqrt{3}}$
- B$tan \phi = \frac{2}{\sqrt{3}}$
- C$tan \phi = \frac{\sqrt{3}}{2}$
- D$tan \phi = -\frac{\sqrt{3}}{2}$
$\left(\frac{sin \theta}{sin \phi}\right)^2 = \frac{tan \theta}{tan \phi}$
$\therefore \left(\frac{sin \theta}{sin \phi}\right)^2 = \frac{sin \theta}{cos \phi} \times \frac{cos \phi}{sin \phi}$
$\therefore\frac{sin \theta}{sin \phi} = \frac{cos \phi}{cos \theta}$
$\therefore sin \theta cos \theta = sin \phi cos \phi$
$\therefore 2sin\theta cos\theta = 2sin\phi cos\phi$
$\therefore sin 2\theta = sin2\phi$
$\therefore \frac{2 tan \theta}{1 + tan^2\theta} = \frac{2tan\phi}{1+ tan^2\phi}$
$tan \theta = 3 tan\phi$ રકમ પરથી
$\therefore \frac{6 tan\phi}{1 +9tan\phi} = \frac{2tan\phi}{1+tan^2 \phi}$
$\therefore 3 (1 + tan^2\phi) = 1 + 9 tan^2\phi$
$\therefore 6 tan^2\phi = 2$ આથી $tan^2\phi = \frac{1}{3}$
$\therefore tan \phi = \pm \frac{1}{\sqrt{3}}$ અને $tan \phi = \pm {\sqrt{3}}$
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