\(E=\dfrac{cos^2a-sin^2a}{\left(sin^2a+cos^2a\right)^2-2\cdot sin^2a\cdot cos^2a-sin^2a-1}\)
\(=\dfrac{1-2sin^2a}{1-1-2\cdot sin^2a\cdot cos^2a-sin^2a}\)
\(=\dfrac{2cos^2a-1}{-sin^2a\left(2cos^2a+1\right)}\)
\(\text{2}\sin^3x-3\sin^{\text{2}}x\cos x+4\sin x\cos^{\text{2}}x-\sin x\cos x+6\cos^3x=7\)
Giải các phương trình sau:
1) sin2x + sin23x - 3cos22x = 0
2) sin22x + sin24x = sin26x
3) cos4x - 5sin4x = 1
4) sin24x + sin23x = cos22x +cos2x với x∈(0;π)
5) 4sin3x - 1 = 3 - √3cos3x
6)sin2x = cos22x + cos23x
Giải phương trình:
a, sinx + sin2x + sin3x + sin4x = cosx + cos2x + cos3x + cos4x
b, cosx.cox2x.cos4x.cos8x=1/16
c, 1/cosx + 1/sin2x = 2/sin4x
Giải các pt sau:
a) \(3\left(\sin x+\cos x\right)-4\sin x\cos x=0\)
b) \(12\left(\sin x-\cos x\right)-\sin2x=2\)
Giải các phương trình :
1) \(\frac{\sin^4x+\cos^4x}{\sin2x}=\frac{1}{2}\left(\tan x+\cot2x\right)\)
2) \(\frac{1}{\sin x}+\frac{1}{\sin\left(x-\frac{3\pi}{2}\right)}=4\sin\left(\frac{7\pi}{4}-x\right)\)
3)\(2\left(\cos^42x-\sin^42x\right)+\cos8x-\cos4x=0\)
4)\(\frac{\sin^4x+\cos^4x}{5\sin2x}=\frac{1}{2}\cot2x-\frac{1}{8\sin2x}\)
5)\(\sin^4x+\cos^4x-3\sin2x+\frac{5}{2}\sin^22x=0\)
1)\(sin^23x.cos2x+sin^2x=0\)
2)
\(cos^23x+cos^22x=sin^2x\)
3)
\(\frac{1}{4}+cos^2\frac{x}{3}=\frac{1}{2}sin^2\frac{x}{2}\)
4)
\(sin^23x-sin^22x-sin^2x=0\)
5)
\(2cos^2x=3sin^25x+2\)
6) 3cosx+2cos2x-cos3x=2sinxsin2x-1
7) \(sinx+cosx=\sqrt{2}\left(2-sin^32x\right)\)
Giải phương trình sau:
a) $\tan ^2x+4\cos ^2x+7=4\tan x+8\cot x$
b) $6\sin ^2x+2\cos ^2x-2\sqrt{3}\sin 2x=14\sin \left(x-\frac{\pi }{6}\right)$
4(sin^4x+cos^4x)-8(sin^6x+cos^6x)-sin^2*4x)=0 Ai giải dùm vs ạ đang cần gấp
1) \(sin^2\left(\frac{x}{2}-\frac{\pi}{4}\right).tan^2x-cos^2\frac{x}{2}=0\)
2) \(tanx=sin^2x\left(c-\frac{\pi}{2010}\right)+cos^2\left(2x+\frac{\pi}{2010}\right)+sinx.sin\left(3x+\frac{\pi}{1005}\right)\)
3) \(1+2cosx\left(sinx-1\right)+\sqrt{2}sinx+4cosx.sin^2\frac{x}{2}=0\)
4) \(3cos4x-8cos^6x+2cos4x=3\)
5) \(1+sinx.sin2x-cosx.sin^22x=2cos^2\left(\frac{\pi}{4}-x\right)\)
6) \(sinx.sin4x=\sqrt{2}cos\left(\frac{\pi}{6}-x\right)-4\sqrt{3}cos^2x.sinx.cos2x\)
7) \(\frac{tan^2x+tanx}{tan^2x+1}=\frac{\sqrt{2}}{2}sin\left(x+\frac{\pi}{4}\right)\)
8) \(cos^4x+sin^4x+cos\left(x-\frac{\pi}{4}\right).sin\left(3x-\frac{\pi}{4}\right)-\frac{3}{2}=0\)
