Question

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

Answer 1

SOLUTION :  

Given : cos 2θ = sin 4θ, where 2θ and 4θ are acute angles.

cos 2θ = sin 4θ

sin ( 90° - 2θ) = sin 4θ

[We know that , sin (90 - 2θ) = cos θ]

On equating both sides, we get  

( 90° - 2θ) = 4θ

90° = 4θ + 2θ

6θ = 90°

θ = 90° / 6

θ = 15°

Hence, the value of θ is 15° .

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Answer 2

$\huge \red{answer} \\ \\ 15 \degree$

$\pink{solution}$
In the questions Given

cos 2θ = sin 4θ, where 2θ and 4θ are acute angles.

Find :

the value of θ.

Now according to questions.

cos 2θ = sin 4θ ... 1

sin ( 90° - 2θ) = sin 4θ ...2

From the trigonometric ratios formula.
$Sin ( 90 - \theta ) = cos \theta$
Comparing the equation both side we get .

sin( 90° - 2θ) = sin4θ

90° = 4θ + 2θ

6θ = 90°

$\theta \: = \frac{90 \degree }{6} \\ \\ \theta \: = 15 \degree$

Therefore the value of θ = 15°.

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