If $ an heta+ an 2 heta+\sqrt{3} an heta an 2 heta=\sqrt{3}$, then the general values of $ heta$ are

Question

If $	an 	heta+	an 2 	heta+\sqrt{3} 	an 	heta 	an 2 	heta=\sqrt{3}$, then the general values of $	heta$ are

Aicharya · Accepted Answer

It is given that $ \begin{aligned} & 	an 	heta+	an 2 	heta+\sqrt{3} 	an 	heta 	an 2 	heta=\sqrt{3} \ & \Rightarrow \frac{	an 	heta+	an 2 	heta}{1-	an 	heta 	an 2 	heta}=\sqrt{3}=	an \frac{\pi}{3} \ & \Rightarrow 	an (3 	heta)=	an \frac{\pi}{3} \Rightarrow 3 	heta=n \pi+\frac{\pi}{3}, n \in Z \ & \Rightarrow 	heta=(3 n+1) \frac{\pi}{9}, n \in Z \end{aligned} $ Hence, option (b) is correct

If $\tan \theta+\tan 2 \theta+\sqrt{3} \tan \theta \tan 2 \theta=\sqrt{3}$, then the general values of…

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