Question

If tan 2θ = cot (θ + 60°), where 2θ and (θ + 6°) an acute angles, find the value of θ.

Answer 1

Given: tan2θ = cot(θ + 60°)

$$\begin{gathered} \tan 2\theta =\cot \left(\theta +60°\right) \\ \Rightarrow \cot \left(90°-2\theta \right)=\cot \left(\theta +60°\right)\left(\because \tan \theta =\cot \left(90°-\theta \right)\right) \\ \Rightarrow 90°-2\theta =\theta +60° \\ \Rightarrow 90°-60°=\theta +2\theta \\ \Rightarrow 3\theta =30° \\ \Rightarrow \theta =\frac{30°}{3} \\ \Rightarrow \theta =10° \\ \mathrm{Hence},\mathrm{the}\mathrm{value}\mathrm{of}\theta \mathrm{is}10°. \end{gathered}$$