The general solution of the equation cot thet | vedclass

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(B) Given equation: $\cot 	heta - 	an 	heta = 2$ Using $\cot 	heta = \frac{1}{	an 	heta}$,we get: $\frac{1}{	an 	heta} - 	an 	heta = 2$ $\Ri

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$\frac{n\pi}{2} + \frac{\pi}{8}$

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(B) Given equation: $\cot 	heta - 	an 	heta = 2$ Using $\cot 	heta = \frac{1}{	an 	heta}$,we get: $\frac{1}{	an 	heta} - 	an 	heta = 2$ $\Rightarrow \frac{1 - 	an^2 	heta}{	an 	heta} = 2$ $\Rightarrow 1 - 	an^2 	heta = 2 	an 	heta$ $\Rightarrow 	an^2 	heta + 2 	an 	heta - 1 = 0$ Alternatively,using $\cot 	heta - 	an 	heta = \frac{\cos 	heta}{\sin 	heta} - \frac{\sin 	heta}{\cos 	heta} = \frac{\cos^2 	heta - \sin^2 	heta}{\sin 	heta \cos 	heta} = \frac{\cos 2	heta}{\frac{1}{2} \sin 2	heta} = 2 \cot 2	heta$ So,$2 \cot 2	heta = 2 \Rightarrow \cot 2	heta = 1$ $\Rightarrow 	an 2	heta = 1 = 	an \frac{\pi}{4}$ General solution for $	an x = 	an \alpha$ is $x = n\pi + \alpha$ Therefore,$2	heta = n\pi + \frac{\pi}{4}$ $\Rightarrow 	heta = \frac{n\pi}{2} + \frac{\pi}{8}$

The general solution of the equation $\cot \theta - \tan \theta = 2$ is

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