If 29 tan theta = 31, then the value of frac{ | vedclass

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(D) Given,$29 	an 	heta = 31 \implies 	an 	heta = \frac{31}{29}$.Since $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$,we have $\frac{\sin 	heta}

Vedclass · Accepted Answer

$900$

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(D) Given,$29 	an 	heta = 31 \implies 	an 	heta = \frac{31}{29}$.Since $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$,we have $\frac{\sin 	heta}{\cos 	heta} = \frac{31}{29}$.Using the property of ratios,we can write $\frac{\sin 	heta + \cos 	heta}{\sin 	heta - \cos 	heta} = \frac{31 + 29}{31 - 29} = \frac{60}{2} = 30$.Now,consider the expression $\frac{1+2 \sin 	heta \cos 	heta}{1-2 \sin 	heta \cos 	heta}$.We know that $1 = \sin^2 	heta + \cos^2 	heta$,so the expression becomes:$\frac{\sin^2 	heta + \cos^2 	heta + 2 \sin 	heta \cos 	heta}{\sin^2 	heta + \cos^2 	heta - 2 \sin 	heta \cos 	heta} = \frac{(\sin 	heta + \cos 	heta)^2}{(\sin 	heta - \cos 	heta)^2}$.Substituting the value found earlier:$= \left( \frac{\sin 	heta + \cos 	heta}{\sin 	heta - \cos 	heta} ight)^2 = (30)^2 = 900$.

If $29 \tan \theta = 31,$ then the value of $\frac{1+2 \sin \theta \cos \theta}{1-2 \sin \theta \cos \theta}$ is equal to

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