Question

1-2,5(sinx+cosx)=0, найти x

Answer 1

$1-2,5(sinx+cosx)=0\Leftrightarrow 2,5(sinx+cosx)=1\Leftrightarrow \\\Leftrightarrow 2,5\sqrt{2}sin\left ( x+\frac{\pi}{4} \right )=1\Leftrightarrow sin\left ( x+\frac{\pi}{4} \right )=\frac{1}{2,5\sqrt{2}}\Leftrightarrow \\\Leftrightarrow x+\frac{\pi}{4}=(-1)^k\cdot arcsin\left ( \frac{\sqrt{2}}{5} \right )+\pi k\Leftrightarrow \\\Leftrightarrow x=(-1)^k\cdot arcsin\left ( \frac{\sqrt{2}}{5} \right )-\frac{\pi}{4}+\pi k,k\in \mathbb{Z}$