cos
2
a−sin
a=cos2a,→sin
a−cos
a=−cos2a
\begin{gathered}sin^{2}\frac{x}{4}-cos^{2}\frac{x}{4}=-cos\frac{x}{2} \\ cos\frac{x}{2}=-\frac{1}{2} , \\\frac{x}{2}=\pm(pi-\frac{pi}{3})+2pi\cdot{n} , n\in{Z} \\ x=\pm\frac{4pi}{3}+4pi\cdot{n}\end{gathered}
sin
4
x
−cos
=−cos
=−
1
,
=±(pi−
3
pi
)+2pi⋅n,n∈Z
x=±
4pi
+4pi⋅n
Наиболший отрицателный корень x=-\frac{4pi}{3}x=−
cos
2
a−sin
2
a=cos2a,→sin
2
a−cos
2
a=−cos2a
\begin{gathered}sin^{2}\frac{x}{4}-cos^{2}\frac{x}{4}=-cos\frac{x}{2} \\ cos\frac{x}{2}=-\frac{1}{2} , \\\frac{x}{2}=\pm(pi-\frac{pi}{3})+2pi\cdot{n} , n\in{Z} \\ x=\pm\frac{4pi}{3}+4pi\cdot{n}\end{gathered}
sin
2
4
x
−cos
2
4
x
=−cos
2
x
cos
2
x
=−
2
1
,
2
x
=±(pi−
3
pi
)+2pi⋅n,n∈Z
x=±
3
4pi
+4pi⋅n
Наиболший отрицателный корень x=-\frac{4pi}{3}x=−
3
4pi