Question

ТЕРМІНОВО Спростити 1-sin((a/2) - 3π) - cos²a/4=sin²a/4​

Answer 1

$1-\sin(\frac{\alpha}{2} - 3\pi) - \cos^2\frac{\alpha}{4} = \sin^2\frac{\alpha}{4}\\\\1+\sin\frac{\alpha}{2} - \cos^2\frac{\alpha}{4} - \sin^2\frac{\alpha}{4} = 0\\\\1+\sin\frac{\alpha}{2} - (\cos^2\frac{\alpha}{4} + \sin^2\frac{\alpha}{4}) = 0\\\\1 + \sin\frac{\alpha}{2} - 1 = 0\\\\\sin\frac{\alpha}{2} = 0\\\\\frac{\alpha}{2} = \pi k, k \in \mathbb{Z}\\\\\boxed{\alpha = 2\pi k}$

ответ: $2\pi k, k \in \mathbb{Z}$.