Question

Cos^2x-sin^2x-2cos^2 2x=0

Answer 1

Есть формула косинуса двойного угла:
$cos^2a-sin^2a=cos2a$

$cos^2x-sin^2x-2cos^2 2x=0\\\\cos2x-2cos^22x=0\\\\2cos^22x-cos2x=0\\\\cos2x(2cos2x-1)=0\\\\ \left[\begin{array}{ccc}cos2x=0\\2cos2x-1=0\end{array}\right\rightarrow \left[\begin{array}{ccc}\displaystyle 2x=\frac{\pi}2+\pi n;\,\,\,n\in Z\\\displaystyle cos2x=\frac{1}2\end{array}\right\rightarrow$

$\rightarrow \left[\begin{array}{ccc}\displaystyle x=\frac{\pi}4+\frac{\pi n}2;\,\,\,n\in Z\\\\\displaystyle 2x=б\frac{\pi}3+2\pi n;\,\,\,n\in Z\end{array}\right\rightarrow \boxed{\left[\begin{array}{ccc}\displaystyle x=\frac{\pi}4+\frac{\pi n}2;\,\,\,n\in Z\\\\\displaystyle x=б\frac{\pi}6+\pi n;\,\,\,n\in Z\end{array}\right}$