Question

If sin(50degree - 3/2 alpha) = cos (3alpha-50degree) then find the value of alpha

Answer 1

$$\begin{gathered} \sin \left(50°-\frac{3\mathrm{\alpha }}{2}\right)=\cos \left(3\mathrm{\alpha }-50°\right) \\ \Rightarrow \sin \left(50°-\frac{3\mathrm{\alpha }}{2}\right)=\sin \left[90°-\left(3\mathrm{\alpha }-50°\right)\right]\left[\mathrm{as},\cos \mathrm{\theta }=\sin \left(90°-\mathrm{\theta }\right)\right] \\ \Rightarrow \sin \left(50°-\frac{3\mathrm{\alpha }}{2}\right)=\sin \left(140°-3\mathrm{\alpha }\right) \\ \Rightarrow \left(50°-\frac{3\mathrm{\alpha }}{2}\right)=\left(140°-3\mathrm{\alpha }\right) \\ \Rightarrow 3\mathrm{\alpha }-\frac{3\mathrm{\alpha }}{2}=140°-50° \\ \Rightarrow \frac{3\mathrm{\alpha }}{2}=90° \\ \Rightarrow \mathrm{\alpha }=60° \end{gathered}$$