\(\Leftrightarrow1-cos\left(2x+\frac{2\pi}{3}\right)+1-cos\left(2x+\frac{4\pi}{3}\right)=3-sinx\)
\(\Leftrightarrow cos\left(2x+\frac{2\pi}{3}\right)+cos\left(2x+\frac{4\pi}{3}\right)=sinx-1\)
\(\Leftrightarrow2cos\left(2x+\pi\right)cos\left(\frac{\pi}{3}\right)=sinx-1\)
\(\Leftrightarrow-cos2x=sinx-1\)
\(\Leftrightarrow-\left(1-2sin^2x\right)=sinx-1\)
\(\Leftrightarrow2sin^2x=sinx\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\sinx=\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow...\)
\(\cos\left(x+\frac{\pi}{3}\right)+\cos x=\frac{3}{2}-4\sin\left(\frac{x}{2}\right)\cdot\sin\left(\frac{x}{2}+\frac{\pi}{6}\right)\)
\(2\sin^2\left(5\pi+1\right)-\left(\sqrt{3}+1\right)\sin2\left(\frac{\pi}{2}-x\right)+\sqrt{3}\sin^2\left(\frac{9\pi}{2}+x\right)=0\)
\(2\sin\left(\frac{\pi}{4}+x\right)+\sin\left(x-\frac{\pi}{4}\right)=\frac{3\sqrt{2}}{2}\)
\(2\sin\left(\frac{\pi}{4}+x\right)+\sin\left(x-\frac{\pi}{4}\right)=\frac{3\sqrt{2}}{2}\)
giải phương trình
\(\sin x\sqrt{1+2\sin x}=\cos2x\)
\(\sin\left(\frac{5x}{2}-\frac{\pi}{4}\right)-\cos\left(\frac{x}{2}-\frac{\pi}{4}\right)=\sqrt{2}\cos\frac{3x}{2}\)
\(3\sqrt{\tan x+1}\left(\sin x+2\cos x\right)=5\left(\sin x+3\cos x\right)\)
\(\sqrt{2}\left(\sin x+\sqrt{3}\cos x\right)=\sqrt{3}\cos2x-\sin2x\)
\(\sin2x\sin4x+2\left(3\sin x-4\sin^2x+1\right)=0\)
sin3x=\(\frac{-\sqrt{3}}{2}\)
\(sin\left(2x-\frac{\pi}{7}\right)=\frac{\sqrt{2}}{2}\)
\(sin\left(4x+1\right)=\frac{3}{5}\)
\(sin\left(2x+\frac{\pi}{7}\right)=sin\left(x-\frac{3\pi}{7}\right)\)
\(sin\left(4x+\frac{\pi}{7}\right)=\frac{1}{4}\)
MỌI NGƯỜI GIÚP MÌNH VỚI MÌNH CẢM ƠN NHIỀU
Giải phương trình: \(\sin\left(\frac{3\pi}{10}-\frac{x}{2}\right)=\frac{1}{2}\sin\left(\frac{\pi}{10}+\frac{3x}{2}\right)\)
Giải phương trình:
a) \(tan\left(\frac{\pi}{2}sin\pi\left(x+1\right)\right)=1\)
b) \(tan\left(\frac{\pi}{3}cot\pi x\right)=\frac{1}{\sqrt{3}}\)
c) \(sin\left(\pi tan3x\right)=\frac{1}{2}\)
Mọi người giúp em với, em cảm ơn ạ
Bài tập quy về dạng phương trình cơ bản:
\(1.\sin\left(x-\frac{\pi}{3}\right)+2cos\left(x-\frac{\pi}{6}\right)=0\);
\(2.\sin^23x=cos^2x\);
\(3.sin\left(2x-\frac{7\pi}{2}\right)+cos2x=1\)
\(4.\sqrt{2}cos\left(x-\frac{3\pi}{4}\right)=1+sinx\)
\(5.\sin\left(2x-\frac{7\pi}{2}\right)+cós2x=1\)