If cot theta + cot left( {frac{pi }{4} + thet | vedclass

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Question

(d) $\cot 	heta + \cot \left( {\frac{\pi }{4} + 	heta } ight) = 2$

$ \Rightarrow \frac{{\cos 	heta }}{{\sin 	heta }} + \frac{{\cos \{ (\pi /4

Vedclass · Accepted Answer

$n\pi \pm \frac{\pi }{6}$

Vedclass · Answer

(d) $\cot 	heta + \cot \left( {\frac{\pi }{4} + 	heta } ight) = 2$

$ \Rightarrow \frac{{\cos 	heta }}{{\sin 	heta }} + \frac{{\cos \{ (\pi /4) + 	heta \} }}{{\sin \{ (\pi /4) + 	heta \} }} = 2$

$ \Rightarrow $ $\sin \left( {\frac{\pi }{4} + 2	heta } ight) = 2\sin 	heta \sin \left( {\frac{\pi }{4} + 	heta } ight)$

$ \Rightarrow $ $\sin \left( {\frac{\pi }{4} + 2	heta } ight) + \cos \left( {\frac{\pi }{4} + 2	heta } ight) = \frac{1}{{\sqrt 2 }}$

$ \Rightarrow $ $\cos 2	heta = \frac{1}{2} $

$\Rightarrow 2	heta = 2n\pi \pm \frac{\pi }{3} $

$\Rightarrow 	heta = n\pi \pm \frac{\pi }{6}$.

If $\cot \theta + \cot \left( {\frac{\pi }{4} + \theta } \right) = 2$, then the general value of $\theta $ is

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