\(\Leftrightarrow sin\left(x+\dfrac{\Pi}{4}\right)=-sin\left(x-\dfrac{\Pi}{3}\right)\)
\(\Leftrightarrow sin\left(x+\dfrac{\Pi}{4}\right)=sin\left(\dfrac{\Pi}{3}-x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{\Pi}{4}=\dfrac{\Pi}{3}-x+k2\Pi\\x+\dfrac{\Pi}{4}=\dfrac{2}{3}\Pi+x+k2\Pi\end{matrix}\right.\Leftrightarrow x=\dfrac{\Pi}{24}+k\Pi\)
bài 1: a) \(sin\left(2x+\dfrac{\pi}{6}\right)+sin\left(x-\dfrac{\pi}{3}\right)=0\)
b) \(sin\left(2x-\dfrac{\pi}{3}\right)-cos\left(x+\dfrac{\pi}{3}\right)=0\)
c) \(sin\left(2x+\dfrac{\pi}{3}\right)+cos\left(x-\dfrac{\pi}{6}\right)=0\)
1) sin\(\sin\left[\pi sin2x\right]\)=1
2) cos\(\left[\dfrac{\pi}{2}.cos\left(x-\dfrac{\pi}{4}\right)\right]\)=\(\dfrac{\sqrt{2}}{2}\)
3) sin(x+24*) + sin(x+144*) = cos20*
Nghiệm của phương trình \(sin^4x+cos^4x+cos\left(x-\dfrac{\pi}{4}\right).sin\left(3x-\dfrac{\pi}{4}\right)-\dfrac{3}{2}=0\)
Tìm nghiệm của các phương trinh:
1,\(\left(sinx+\dfrac{sin3x+cos3x}{1+2sin2x}\right)=\dfrac{3+cos2x}{5}\)
2,\(48-\dfrac{1}{cos^4x}-\dfrac{2}{sin^2x}\left(1+cot2xcotx\right)=0\)
3,\(cos^4x+sin^4x+cos\left(x-\dfrac{\pi}{4}\right)sin\left(3x-\dfrac{\pi}{4}\right)-\dfrac{3}{2}=0\)
4,\(cos5x+cos2x+2sin3xsin2x=0\) trên \(\left[0;2\pi\right]\)
5,\(\dfrac{cos\left(cosx+2sinx\right)+3sinx\left(sinx+\sqrt{2}\right)}{sin2x-1}=1\)
6,\(\left(sinx+\dfrac{sin3x+cos3x}{1+2sin2x}\right)=\dfrac{3+cos2x}{5}\)
7,\(cos\left(2x+\dfrac{\pi}{4}\right)+cos\left(2x-\dfrac{\pi}{4}\right)+4sinx=2+\sqrt{2}\left(1-sinx\right)\)
Giải các phương trình:
a) \(\left|\sin x+\dfrac{1}{2}\right|=\dfrac{1}{2}\)
b) \(\tan^2\left(x+\dfrac{\pi}{6}\right)=3\)
c) \(2\sin\left(4x-\dfrac{\pi}{3}\right)-1=0\)
\(\sin^4x+\sin^4\left(x+\dfrac{\Pi}{4}\right)+\sin^4\left(x-\dfrac{\Pi}{4}\right)=\dfrac{5}{4}\)
giải giúp em với em đang cần gấp ạ
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) \(2\sqrt{2}sin^2x-sin2x=0\)
bài 1:
a) \(cos\left(2x-\dfrac{\pi}{6}\right)+cos\left(x+\dfrac{\pi}{3}\right)=0\)
b) \(cos\left(2x+30^o\right)+sin\left(x-30^o\right)=0\)
\(3sin\left(\dfrac{x}{2}+\dfrac{\pi}{6}\right)+sin\left(\dfrac{3x}{2}-\dfrac{\pi}{6}\right)=0\)
tìm tập xác định của hàm số lượng giác sau
a)\(y=\dfrac{tan\left(2x-\dfrac{\pi}{4}\right)}{\sqrt{1-sin\left(x-\dfrac{\pi}{8}\right)}}\)
b)\(y=\dfrac{tan\left(x-\dfrac{\pi}{4}\right)}{1-cos\left(x+\dfrac{\pi}{3}\right)}\)
c)\(y=\dfrac{3}{cosx-cos3x}\)
d)\(y=\dfrac{4}{sin^2x-cos^2x}\)
e)\(y=\dfrac{1+cot\left(\dfrac{\pi}{3}+x\right)}{tan^2\left(3x-\dfrac{\pi}{4}\right)}\)
