सिद्ध कीजिए कि,$\tan \theta + \tan (90^{\circ} - \theta) = \sec \theta \sec (90^{\circ} - \theta)$

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(N/A) बायाँ पक्ष ($L$.$H$.$S$.) $= \tan \theta + \tan (90^{\circ} - \theta)$
चूँकि $\tan (90^{\circ} - \theta) = \cot \theta$,इसलिए:
$= \tan \theta + \cot \theta$
$= \frac{\sin \theta}{\cos \theta} + \frac{\cos \theta}{\sin \theta}$
$= \frac{\sin^2 \theta + \cos^2 \theta}{\sin \theta \cos \theta}$
चूँकि $\sin^2 \theta + \cos^2 \theta = 1$,इसलिए:
$= \frac{1}{\sin \theta \cos \theta}$
$= \frac{1}{\cos \theta} \cdot \frac{1}{\sin \theta}$
$= \sec \theta \operatorname{cosec} \theta$
चूँकि $\operatorname{cosec} \theta = \sec (90^{\circ} - \theta)$,इसलिए:
$= \sec \theta \sec (90^{\circ} - \theta) = \text{दायाँ पक्ष (R.H.S.)}$

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