If 1+cos^{2} theta = 3 sin theta cos theta,th | vedclass

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Question

(B) Given equation: $1 + \cos^{2} 	heta = 3 \sin 	heta \cos 	heta$.Divide both sides by $\cos^{2} 	heta$ (since $\cos 	heta 
eq 0$ for $0 < 	he

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given equation: $1 + \cos^{2} 	heta = 3 \sin 	heta \cos 	heta$.Divide both sides by $\cos^{2} 	heta$ (since $\cos 	heta 
eq 0$ for $0 $\frac{1}{\cos^{2} 	heta} + \frac{\cos^{2} 	heta}{\cos^{2} 	heta} = 3 \frac{\sin 	heta \cos 	heta}{\cos^{2} 	heta}$.$\sec^{2} 	heta + 1 = 3 	an 	heta$.Using the identity $\sec^{2} 	heta = 1 + 	an^{2} 	heta$:$(1 + 	an^{2} 	heta) + 1 = 3 	an 	heta$.$	an^{2} 	heta - 3 	an 	heta + 2 = 0$.Factor the quadratic equation:$(	an 	heta - 1)(	an 	heta - 2) = 0$.So,$	an 	heta = 1$ or $	an 	heta = 2$.If $	an 	heta = 1$,then $\cot 	heta = \frac{1}{	an 	heta} = 1$.If $	an 	heta = 2$,then $\cot 	heta = \frac{1}{2} = 0.5$.Since the question asks for the integral value,the correct value is $1$.

If $1+\cos^{2} \theta = 3 \sin \theta \cos \theta$,then the integral value of $\cot \theta$ is $(0 < \theta < \frac{\pi}{2})$.

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