(sin theta + cos theta)(tan theta + cot theta | vedclass

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Question

(C) Given expression: $(\sin 	heta + \cos 	heta)(	an 	heta + \cot 	heta)$ $= (\sin 	heta + \cos 	heta) \left( \frac{\sin 	heta}{\cos 	heta} +

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$\sec 	heta + \operatorname{cosec} 	heta$

Vedclass · Answer

(C) Given expression: $(\sin 	heta + \cos 	heta)(	an 	heta + \cot 	heta)$ $= (\sin 	heta + \cos 	heta) \left( \frac{\sin 	heta}{\cos 	heta} + \frac{\cos 	heta}{\sin 	heta} ight)$ $= (\sin 	heta + \cos 	heta) \left( \frac{\sin^2 	heta + \cos^2 	heta}{\sin 	heta \cos 	heta} ight)$ Since $\sin^2 	heta + \cos^2 	heta = 1$,we have: $= (\sin 	heta + \cos 	heta) \left( \frac{1}{\sin 	heta \cos 	heta} ight)$ $= \frac{\sin 	heta}{\sin 	heta \cos 	heta} + \frac{\cos 	heta}{\sin 	heta \cos 	heta}$ $= \frac{1}{\cos 	heta} + \frac{1}{\sin 	heta}$ $= \sec 	heta + \operatorname{cosec} 	heta$

$(\sin \theta + \cos \theta)(\tan \theta + \cot \theta)$ is equal to

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