Prove that,(sin alpha+cos alpha)(tan alpha+co | vedclass

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$LHS$ $= (\sin \alpha + \cos \alpha)(	an \alpha + \cot \alpha)$$= (\sin \alpha + \cos \alpha) \left( \frac{\sin \alpha}{\cos \alpha} + \frac{\cos \al

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$LHS$ $= (\sin \alpha + \cos \alpha)(	an \alpha + \cot \alpha)$$= (\sin \alpha + \cos \alpha) \left( \frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} ight)$ $\left[ \because 	an \alpha = \frac{\sin \alpha}{\cos \alpha} 	ext{ and } \cot \alpha = \frac{\cos \alpha}{\sin \alpha} ight]$$= (\sin \alpha + \cos \alpha) \left( \frac{\sin^2 \alpha + \cos^2 \alpha}{\sin \alpha \cos \alpha} ight)$$= (\sin \alpha + \cos \alpha) \cdot \frac{1}{\sin \alpha \cos \alpha}$ $\left[ \because \sin^2 \alpha + \cos^2 \alpha = 1 ight]$$= \frac{\sin \alpha}{\sin \alpha \cos \alpha} + \frac{\cos \alpha}{\sin \alpha \cos \alpha}$$= \frac{1}{\cos \alpha} + \frac{1}{\sin \alpha}$$= \sec \alpha + \operatorname{cosec} \alpha = 	ext{RHS}$

Prove that,$(\sin \alpha+\cos \alpha)(\tan \alpha+\cot \alpha)=\sec \alpha+\operatorname{cosec} \alpha$

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