If $\cos \theta \neq 0$, and $\sec \theta-1=(\sqrt{2}-1) \tan \theta$ then $\theta=$

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Aicharya · Accepted Answer

If $\cos \theta \neq 0$ and $\sec \theta-1=(\sqrt{2}-1) \tan \theta$ $\begin{array}{ll} \Rightarrow \quad \frac{1-\cos \theta}{\cos \theta}=(\sqrt{2}-1) \frac{\sin \theta}{\cos \theta} \ \Rightarrow \quad 2 \sin ^2 \frac{\theta}{2}=(\sqrt{2}-1) 2 \sin \frac{\theta}{2} \cos \frac{\theta}{2} \end{array}$ $\Rightarrow \text{Either } \sin \frac{\theta}{2}=0 \text { or } \tan \frac{\theta}{2}=\sqrt{2}-1$ $\Rightarrow \text{Either } \frac{\theta}{2}=n \pi, n \in Z$ $\text{or } \frac{\theta}{2}=n \pi+\frac{\pi}{8}, n \in Z$ $\Rightarrow \quad \theta=2 n \pi+\frac{\pi}{4}$ or $2 n \pi, n \in Z$ Hence, option (2) is correct.

If \(\cos \theta \neq 0\), and \(\sec \theta-1=(\sqrt{2}-1) \tan \theta\) then \(\theta=\)

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