If $ \cos 2 \theta=\sin 4 \theta $, where $ 2 \theta $ and $ 4 \theta $ are acute angles, find the value of $ \theta $.

Given:

\( \cos 2 \theta=\sin 4 \theta \), where \( 2 \theta \) and \( 4 \theta \) are acute angles.

To do:

We have to find the value of \( \theta \).

Solution:  

We know that,

$\cos\ (90^{\circ}- \theta) = sin\ \theta$

Therefore,

$\cos 2 \theta=\sin 4 \theta$

$\cos 2\theta=cos\ (90^{\circ}- 4\theta)$

Comparing on both sides, we get,

$90^{\circ}- 4\theta=2\theta$

$4\theta+2\theta=90^{\circ}$

$6\theta=90^{\circ}$

$\theta=\frac{90^{\circ}}{6}$

$\theta=15^{\circ}$

The value of \( \theta \) is $15^{\circ}$.  

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Updated on: 10-Oct-2022

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