Solve $sin 2 x + cos 4 x = 2$

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Solution

Given, $sin 2 x + cos 4 x = 2 \Rightarrow sin 2 x + 1 - 2 {sin}^{2} 2 x = 2 \Rightarrow 2 {sin}^{2} 2 x - sin 2 x + 1 = 0$
$\Rightarrow sin 2 x = \frac{1 \pm \sqrt{1 - 4}}{4}$
Imaginary roots hence no solution

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