Question

Find the value of θ in the following : cos 2θ = cos 60° cos 30° + sin 60° sin 30°

Answer 1

Dear student,
Here is the solution of your asked query:
$$\begin{gathered} \cos 2\mathrm{\theta }=\cos 60°\cos 30°+\sin 60°\sin 30° \\ \Rightarrow \cos 2\mathrm{\theta }=\cos \left(60°-30°\right)\{\mathrm{Using}\mathrm{the}\mathrm{identity}\cos \left(\mathrm{A}-\mathrm{B}\right)=\mathrm{cosAcosB}+\mathrm{sinAsinB}\} \\ \Rightarrow \cos 2\mathrm{\theta }=\cos 30° \\ \Rightarrow 2\mathrm{\theta }=30° \\ \Rightarrow \mathrm{\theta }=\frac{30}{2}=15° \end{gathered}$$
Regards