giải các pt
a) \(sinx+cosx-\sqrt{2}sin2x=0\)
b) \(sin^2x+sin2x=3cos^2x\)
c) \(sinx\left(1-sinx\right)=cosx\left(cosx-1\right)\)
d) \(2\left(sin^3x-cos^3x\right)=\sqrt{3}.cos2x\left(sinx-cosx\right)\)
Giải các pt sau
a, \(\dfrac{1}{sinx}+\dfrac{1}{cosx}=4sin\left(x+\dfrac{\pi}{4}\right)\)
b, \(2sin\left(2x-\dfrac{\pi}{6}\right)+4sinx+1=0\)
c, \(cos2x+\sqrt{3}sinx+\sqrt{3}sin2x-cosx=2\)
d, \(4sin^2\dfrac{x}{2}-\sqrt{3}cos2x=1+cos^2\left(x-\dfrac{3\pi}{4}\right)\)
giải phương trình
1.\(sin^3x+2cosx-2+sin^2x=0\)
\(2.\frac{\sqrt{3}}{2}sin2x+\sqrt{2}cos^2x+\sqrt{6}cosx=0\)
3.\(2sin2x-cos2x=7sinx+2cosx-4\)
4.\(2cos2x-8cosx+7=\frac{1}{cosx}\)
5.\(cos^8x+sin^8x=2\left(cos^{10}x+sin^{10}x\right)+\frac{5}{4}cos2x\)
6.\(1+sinx+cos3x=cosx+sin2x+cos2x\)
7.\(1+sinx+cosx+sin2x+cos2x=0\)
Giải phương trình sau
1.\(cos2x-\sqrt{3}sin2x=\sqrt{2}\)
2.\(4sin^2\frac{x}{2}-3\sqrt{3}sinx-2cos^2\frac{x}{2}=4\)
3. \(2\left(sinx+cosx\right)=4sinxcosx+1\)
4. \(cosx-sinx-2sin2x-1=0\)
\(5.\sqrt{3}sin2x+cos2x=2sinx\)
6. \(9sin^2x-5cos^2x-5sinx+4=0\)
7.\(cos^2x-\sqrt{3}sin2x=1+sinx\)
8.\(\frac{3}{cos^2x}=3+2tan^2x\)
Giải các pt sau:
a) \(\dfrac{\sqrt{3}\left(1-cos2x\right)}{2sinx}=cosx\)
b) \(sin2x+sin^2x=\dfrac{1}{2}\)
c) \(cosx+\sqrt{3}sinx=\dfrac{1}{cosx}\)
d) \(cos7x-\sqrt{3}sin7x+\sqrt{2}=0,x\in\left(\dfrac{2\pi}{5};\dfrac{6\pi}{7}\right)\)
1) 2sinx + cosx = sin2x + 1
2) (1 + cosx)(1+sinx) = 2
3) 3cos4x - 8cos6x + 2cos2x +3 =0
4) sin3x + cos3x.sinx + cosx = \(\sqrt{2}\)cos2x
5) (2cosx -1)(2sinx + cosx) = sin2x - sinx
1> 1 + sinx + cosx + sin2x + cos2x = 0
2> cos2x + 3sin2x + 5 sinx - 3cosx = 3
3> \(\dfrac{\sqrt{2}*(cosx - sinx)}{cotx - 1}\) = \(\dfrac{1}{tanx + cot2x}\)
4> (2cosx - 1)*(2sinx + cosx) = sin2x - sinx
Giải phương trình lượng giác
1 , \(\sin2x-2\sqrt{2}\left(sinx+cosx\right)=5\)
2 , \(1+sin\frac{x}{2}sinx-cos\frac{x}{2}sin^2x=2cos^2\left(\frac{\pi}{4}-\frac{x}{2}\right)\)
giải các pt
a) \(sin2x-2\sqrt{3}cos^2x=4cosx\)
b) \(sin^2x-3cos^2x=sinx-\sqrt{3}cosx\)
c) \(sin6x\left(cos3x-1\right)-sin6x.sin3x=0\)
d) \(\left(sin2x-cos2x\right)^2-3\left(sin2x-cos2x\right)-4=0\)
e) \(\frac{sin2x+sin6x}{cos2x}-2cos4x=2\sqrt{2}\)