Find the value of theta,if |tan theta|=tan th | vedclass

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(B) Given equation: $|	an 	heta| = 	an 	heta + \sec 	heta$. Case $1$: If $	an 	heta \ge 0$,then $	an 	heta = 	an 	heta + \sec 	heta$,which

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$\frac{11\pi}{6}$

Vedclass · Answer

(B) Given equation: $|	an 	heta| = 	an 	heta + \sec 	heta$. Case $1$: If $	an 	heta \ge 0$,then $	an 	heta = 	an 	heta + \sec 	heta$,which implies $\sec 	heta = 0$. This has no solution. Case $2$: If $	an 	heta Substituting $	an 	heta = \frac{\sin 	heta}{\cos 	heta}$ and $\sec 	heta = \frac{1}{\cos 	heta}$,we get $2\sin 	heta + 1 = 0$,so $\sin 	heta = -\frac{1}{2}$. Since $	an 	heta Checking $	an 	heta For $	heta = \frac{7\pi}{6}$,$	an 	heta = 	an(\frac{7\pi}{6}) = \frac{1}{\sqrt{3}} > 0$ (Reject). For $	heta = \frac{11\pi}{6}$,$	an 	heta = 	an(\frac{11\pi}{6}) = -\frac{1}{\sqrt{3}} Thus,the solution is $	heta = \frac{11\pi}{6}$.

Find the value of $\theta$,if $|\tan \theta|=\tan \theta+\frac{1}{\cos \theta}$ and $\theta \in[0, 2\pi]-\{\pm \frac{\pi}{2}\}$

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