ĐKXĐ: ...
\(\Leftrightarrow cos4x+\frac{sinx}{cosx}.4sinx.cosx.cos2x=1\)
\(\Leftrightarrow2cos^22x-1+4sin^2x.cos2x=1\)
\(\Leftrightarrow cos^22x+\left(1-cos2x\right)cos2x=1\)
\(\Leftrightarrow cos2x=1\Rightarrow x=k\pi\)
1+sin2x=2(sin^4x+cos^4x)
\(\sin^4x+\cos^4x=1-\frac{1}{2}\sin^22x\)
giải phương trình : \(\cos^4x-\sin^4x+\sqrt{3}\sin2x=1\)
Timg GTNN, GTLN của hàm số:
a) y= 4sin2 x + \(\sqrt{2}\) sin (\(2x+\frac{\pi}{4}\))
b) y= cos x ( 1+cos 2x)
c) y= sin2 x. cos x +cos2 x.sin x
giải các pt
a) \(cos\frac{4x}{3}=cos^2x\)
b) \(cos\frac{8x}{3}=cos^2\frac{2x}{3}\)
c) \(2cos^2\frac{3x}{5}+1=3cos\frac{4x}{5}\)
d) \(cos^2x+\frac{1}{cos^2x}+2=2cosx+\frac{2}{cosx}\)
Giải phương trình
1.\(sin^2\left(x-\frac{\pi}{6}\right)+sin^2\left(x+\frac{\pi}{6}\right)=5cosx-2\)
2.\(4sin^4x+12cos^2x=7\\\)
3.\(sin^4x+cos^{\:4}x=\frac{1}{2}\)
4.\(sin^4x+cos^4x=cos2x\)
\(\frac{2sin5x}{sinx+cosx}+\frac{1}{2}sin2x=sin^4x+cos^4x+sin^2x.cos^2x\)
Giải PT
a) 4sin (3x + \(\frac{\pi}{3}\)) - 2 = 0
b) 4sin ( 4x + 1) -1 = 0
c) sin ( x + \(\frac{x}{4}\)) -1 = 0
d) 2sin ( 2x + 70o) + 1 = 0
e) sin x . cos ( 2x - 3 ) = 0
f) cos 2x -cos 4x = 0
g) cos ( sin 3x) = 1
Giải phương trình:
\(4\left(Sin^4x+Cos^4x\right)+Sin4x-2=0\)
