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