Question

Решите тригонометрическое уравнение:
Cos²2x-Sin²2x+Sin2x-1=0
СРОЧНОО!!!​

Answer 1

$\displaystyle\bf\\Cos^{2}2x-Sin^{2} 2x+Sin2x-1=0\\\\Cos^{2}2x-Sin^{2} 2x+Sin2x-Sin^{2}2x-Cos^{2} 2x =0\\\\-2Sin^{2} 2x+Sin2x=0\\\\2Sin^{2} 2x-Sin2x=0\\\\Sin2x\cdot(2Sin2x-1)=0\\\\\\\left[\begin{array}{ccc}Sin2x=0\\2Sin2x-1=0\end{array}\right\\\\\\\left[\begin{array}{ccc}Sin2x=0\\Sin2x=\dfrac{1}{2} \end{array}\right\\\\\\\left[\begin{array}{ccc}2x=\pi n,n\in Z\\2x=(-1)^{n}arcSin\frac{1}{2}+\pi n,n\in Z \end{array}\right$

$\displaystyle\bf\\\left[\begin{array}{ccc}x=\dfrac{\pi n}{2} ,n\in Z\\2x=(-1)^{n}\dfrac{\pi }{6} +\pi n,n\in Z \end{array}\right\\\\\\\left[\begin{array}{ccc}x=\dfrac{\pi n}{2} ,n\in Z\\x=(-1)^{n}\dfrac{\pi }{12} +\dfrac{\pi n}{2} ,n\in Z \end{array}\right$