(1+tan theta+sec theta)(1+cot theta-operatorn | vedclass

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Question

$(1+	an 	heta+\sec 	heta)(1+\cot 	heta-\operatorname{cosec} 	heta)$

$=\left(1+\frac{\sin 	heta}{\cos 	heta}+\frac{1}{\cos 	heta}ight)\lef

Vedclass · Accepted Answer

$2$

Vedclass · Answer

$(1+	an 	heta+\sec 	heta)(1+\cot 	heta-\operatorname{cosec} 	heta)$

$=\left(1+\frac{\sin 	heta}{\cos 	heta}+\frac{1}{\cos 	heta}ight)\left(1+\frac{\cos 	heta}{\sin 	heta}-\frac{1}{\sin 	heta}ight)$

$=\left(\frac{\cos 	heta+\sin 	heta+1}{\cos 	heta}ight)\left(\frac{\sin 	heta+\cos 	heta-1}{\sin 	heta}ight)$

$=\frac{(\sin 	heta+\cos 	heta)^{2}-(1)^{2}}{\sin 	heta \cos 	heta}$

$=\frac{\sin ^{2} 	heta+\cos ^{2} 	heta+2 \sin 	heta \cos 	heta-1}{\sin 	heta \cos 	heta}$

$=\frac{1+2 \sin 	heta \cos 	heta-1}{\sin 	heta \cos 	heta}$

$=\frac{2 \sin 	heta \cos 	heta}{\sin 	heta \cos 	heta}=2$

$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=..........$

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