# 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

#### 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°

Concept: Trigonometric Ratios of Some Special Angles
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#### APPEARS IN

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

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