Question

Find the value of θ. θ is an acute angle.

2 sin 2θ = 1​

Answer 1

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Answer 2

The value of θ = 15°

Given :

2sin 2θ = 1 where θ is an acute angle.

To find :

The value of θ

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

2sin 2θ = 1

Step 2 of 2 :

Find the value of θ

$\displaystyle \sf 2 \: sin2 \theta = 1$

$\displaystyle \sf{ \implies }sin2 \theta = \frac{1}{2}$

$\displaystyle \sf{ \implies }sin \: 2 \theta = sin \: {30}^{ \circ}$

$\displaystyle \sf{ \implies } 2 \theta = {30}^{ \circ} \: \: \: \bigg[ \: \because \:\theta \: is \: an \: acute \: angle \bigg]$

$\displaystyle \sf{ \implies } \theta = {15}^{ \circ}$

Hence the required value of θ = 15°

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