\(2\cos4x+4\sin2x.\cos2x-\sqrt{2}=0\\ < =>2.\cos4x+2.\sin4x=\sqrt{2}\\ < =>2\sqrt{2}\sin\left(x+\dfrac{\pi}{4}\right)=\sqrt{2}\\ < =>\sin\left(4x+\dfrac{\pi}{4}\right)=\dfrac{1}{2}\\ < =>\left[{}\dfrac{x+\dfrac{\pi}{4}=\dfrac{\pi}{6}+k2\pi}{x+\dfrac{\pi}{4}=\dfrac{5\pi}{6}+k2\pi}}\\ < =>\left[{}\begin{matrix}x=\dfrac{-\pi}{12}+k2\pi\\x=\dfrac{7\pi}{12}+k2\pi\end{matrix}\right.\)
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) \(\frac{sin2x+sin6x}{cos2x}-2cos4x=2\sqrt{2}\)
hàm số y=5+4sin2xcos2x có tất cả bao nhiêu giá trị nguyên
Rút gon biểu thức sau:
\(\dfrac{sinx-sin3x}{2cos4x}\)
Giải phương trình:
1) \(tanx-cotx+3cot^22x=5\)
2) \(\frac{sin5x}{sinx}=\frac{cos5x}{cosx}+2cos4x-1\)
giải pt :
a, \(4x^2-6x+1+\dfrac{1}{\sqrt{3}}\sqrt{16x^4+4x^2+1}=0\)
b, \(x^2-3x+1+\dfrac{1}{\sqrt{3}}\sqrt{x^4+x^2+1}=0\)
giải pt:
a, \(2x^2-6x-1=\sqrt{4x+5}\)
b, \(18x^2+6x-29=\sqrt{12x+61}\)
c, \(4x^2-13x+5+\sqrt{3x+1}=0\)
c, \(4x^2-13x+5+\sqrt{3x+1}=0\)
giải phương trình :
a, \(\sqrt{x-3}+\sqrt[3]{x^2+1}+x^2+x-2=0\)
b,\(4x^2+\sqrt{2x+3}=8x+1\)
c, \(2x^2-6x+10-5\left(x-2\right)\sqrt{x+1=0}\)
giải phương trình :
a, \(2x^2-11x+21-3\sqrt[3]{4x-4}=0\)
b, \(\left(3x-2\right)\sqrt{x+1}-x^2-x-2=0\)
c, \(x+4-2\left(\dfrac{x+2}{x-1}\right)\sqrt{\dfrac{x-1}{x+2}}=0\)
a) \(2sin\left(x+\dfrac{\pi}{3}\right)+1=0\)
b) \(1+2sin\left(x-30^o\right)=0\)
c) \(\sqrt{3}+2sin\left(x-\dfrac{\pi}{6}\right)=0\)
d) \(2sin\left(x+10^o\right)+\sqrt{3}=0\)
e) \(\sqrt{2}+2sin\left(x-15^o\right)=0\)
f) \(\sqrt{2}sin\left(x-\dfrac{\pi}{3}\right)+1=0\)
g) \(3+\sqrt{5}sin\left(x+\dfrac{\pi}{3}\right)=0\)
h) \(1+sin\left(x-30^o\right)=0\)
i) \(3+\sqrt{5}sin\left(x-\dfrac{\pi}{6}\right)=0\)
k) \(2\sqrt{2}sin^2x-sin2x=0\)
