Giải các phương trình sau
1. \(sinx.cos\frac{\pi}{8}=\frac{1}{2}\)voi x\(\in\)\(\left[-\frac{3\pi}{2};\pi\right]\)
2. \(sinx.cos\frac{\pi}{8}+cos.sin\frac{\pi}{8}=\frac{1}{2}\)voi x\(\in\)\(\left[-\frac{\pi}{2};2\pi\right]\)
3. \(sin\left(\frac{\pi}{3}-2x\right).cos\left(\frac{x}{3}+\frac{\pi}{6}\right)=0\) voi x\(\in\)\(\left[-\frac{\pi}{3};\frac{5\pi}{3}\right]\)
Giải các pt lượng giác sau
1) \(cos^2\left(x-\frac{\pi}{6}\right)-sin^2\left(x-\frac{\pi}{6}\right)=sin\left(x+\frac{\pi}{3}\right)\)
2) \(sin^4-sin^4\left(x+\frac{\pi}{2}\right)=sin\left(x+\frac{\pi}{3}\right)\)
3) \(8cos^3\left(x-\frac{\pi}{3}\right)-1=0\)
giải pt
a) \(tanx.tan\frac{\pi}{9}=1+tan\frac{\pi}{9}.tan\frac{\pi}{90}+tanx.tan\frac{\pi}{90};\left(-2\pi< x< 2\pi\right)\)
b) \(tan^22x+\frac{1}{cos^22x}=7;\left(0< x< 360^0\right)\)
c) \(tan^3x+\frac{1}{cos^2x}+4\sqrt{3}\left(1+tanx\right)=8+7tanx;\left(-\pi< x< \pi\right)\)
Giải các phương trình sau:
a, sinx+cosx+1+sin2x+cos2x=0
b, sinx(1+cos2x)+sin2x=1+cos2x
c, \(\frac{1}{sinx}+\frac{1}{sin\left(x-\frac{3\pi}{2}\right)}=4sin\left(\frac{7\pi}{4}-x\right)\)
d, sin4x+cos4x=\(\frac{7}{8}cot\left(x+\frac{\pi}{3}\right)cot\left(\frac{\pi}{6}-x\right)\)
\(16cosxcos\left(x+\frac{2\Pi}{3}\right)cos\left(x-\frac{2\Pi}{3}\right)cos\left(3x+\frac{2\Pi}{3}\right)cos\left(3x-\frac{2\Pi}{3}\right)=sin9x\)
giải giúp e câu này với ạ
1) \(\sin^2x-\sin x=2\cos^2x\)
2) \(2\sin^2x+\left(1-\sqrt{3}\right)\cos\left(\frac{5pi}{2}-x\right)-\sin\frac{pi}{3}=0\)
3) \(\cos\left(3x+\frac{pi}{4}\right)=\cos\frac{pi}{8}\)
giải pt
\(sin^2\left(2x+\frac{\pi}{6}\right)-6sin\left(x+\frac{\pi}{6}\right).cos\left(x+\frac{\pi}{6}\right)+2=0\)
\(\sin\left(2x+\frac{\Pi}{6}\right)=\frac{-\sqrt{3}}{2}\left(\frac{\Pi}{2}>x>-\Pi\right)\)
Giair các pt lượng giác sau:
1) \(sin\left(x-\frac{\pi}{4}\right)\left(2cos+\sqrt{2}\right)tan2x=0\)
2) \(tan2x.sinx+3\left(sin-\sqrt{3}tan2x\right)-3\sqrt{3}=0\)
3) \(\frac{cos2x}{sin\left(x+\frac{3\pi}{4}\right)}=\frac{sin\left(x+\frac{3\pi}{4}\right)}{cos2x}\)
4) \(\left(\frac{tanx-1}{tanx+1}+cot2x\right)\left(3tan-\sqrt{3}\right)=0;0< x< \pi\)
giải các pt
a) \(cos^2\left(\frac{\pi}{3}+x\right)+4cos\left(\frac{\pi}{6}-x\right)=4\)
b) \(5cos\left(2x+\frac{\pi}{3}\right)=4sin\left(\frac{5\pi}{6}-x\right)-9\)
c) \(2sin^2x+\sqrt{3}sin2x+2\sqrt{3}sinx+2cosx=2\)
d) \(2sin^2x+\sqrt{3}sin2x+4=4\left(\sqrt{3}sinx+cosx\right)\)
