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\(tan \frac\theta4 = \cfrac{\frac\mu2sin\theta}{\frac\mu2 + \frac\mu2cos\theta} \)Find the value of \( \theta \) |
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Answer» \(tan \frac\theta4 = \cfrac{\frac\mu2sin\theta}{\frac\mu2 + \frac\mu2cos\theta} = \frac{sin\theta}{1+ cos\theta}\) \(= \cfrac{2sin\frac\theta2cos\frac\theta2}{2cos^2\frac\theta2}\) \(= tan \left(\frac\theta2\right)\) \(\therefore \frac\theta4 = \frac\theta2 \) ⇒ \(\theta = 0\) tan θ/4 = tan θ/2 ⇒ θ/4 = nπ + θ/2 ⇒ θ/4 - θ/2 = nπ ⇒ -θ/4 = nπ ⇒ θ = -4nπ, n ∈ \(\mathbb{Z}\) |
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