1.

\(tan \frac\theta4 = \cfrac{\frac\mu2sin\theta}{\frac\mu2 + \frac\mu2cos\theta} \)Find the value of \( \theta \)

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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