Question

if theta and 3heta - 30 degree are acute angles such that tan theta =(3theta - 30 degree), then find the value of sin theta.

Answer 1

$$\begin{gathered} \mathrm{Assuming}\mathrm{question}\mathrm{is} \\ \tan \mathrm{\theta }=\cot \left(3\mathrm{\theta }-30°\right) \\ \tan \mathrm{\theta }=\tan \left(90°-\left(3\mathrm{\theta }-30°\right)\right)\left(\mathrm{Since}\tan \left(90-\mathrm{x}\right)=\cot \mathrm{x}\right) \\ \tan \mathrm{\theta }=\tan \left(120°-3\mathrm{\theta }\right) \\ \mathrm{\theta }=120°-3\mathrm{\theta } \\ 4\mathrm{\theta }=120° \\ \mathrm{\theta }=30°. \\ \sin \mathrm{\theta }=\sin 30°=\frac{1}{2}\mathrm{ANS}... \end{gathered}$$