Sin^2 4x + 1 = sin^2 2x

Ptrinh tương đương vs

$4\sin^2x(2x) \cos^2(2x) + 1 = \sin^2(2x)$

$<-> \sin^2(2x) (4\cos^2(2x) - 1) + 1 = 0$

$<-> \sin^2(2x) [4(1-\sin^2(2x)) - 1] + 1 = 0$

$<-> \sin^2(2x) (3 - 4\sin^2(2x)) + 1 = 0$

$<-> -4\sin^4(2x) + 3\sin^2(2x) + 1 = 0$

$<-> (4\sin^2(2x)+1)(1-\sin^2(2x)) = 0$

Ta thấy $4\sin^2(2x)+1 \geq 1 > 0$ nên ptrinh có nghiệm là $\sin^2(2x) = 1$

$<-> \sin(2x) = \pm 1$ hay $2x = \pm\dfrac{\pi}{2} + 2k\pi$

Vậy $x = \pm \dfrac{\pi}{4} + k\pi$.