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If Cos 20 = Sin 4 θ ,Where 2 θ and 4 θ Are Acute Angles, Then Find the Value of θ - Mathematics

Sum

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

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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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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 7 Trigonometric Ratios of Complementary Angles
Exercise | Q 10 | Page 7
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