Question

If cos 20 = sin 4 θ ,where 2 θ and 4 θ are acute angles, then find the value of θ

Answer 1

We  have 

\[\cos2\theta = \sin4\theta\] 

\[ \Rightarrow \sin\left( 90^\circ- 2\theta \right) = \sin4\theta\] 

\[\text{Comparing  both  sides,   we  get}\] 

\[90^\circ - 2\theta = 4\theta\] 

\[ \Rightarrow 2\theta + 4\theta = 90^\circ\] 

\[ \Rightarrow 6\theta = 90^\circ\] 

\[ \Rightarrow \theta = \frac{90^\circ}{6}\] 

\[ \therefore   \theta = 15^\circ\]

Hence, the value of θ is 15°