\(\Leftrightarrow cos\left(x-\frac{5\pi}{4}\right)=cos\left(\frac{\pi}{2}-x-\frac{3\pi}{4}\right)=cos\left(x+\frac{\pi}{4}\right)\)
\(\Leftrightarrow x-\frac{5\pi}{4}=-x-\frac{\pi}{4}+k2\pi\)
\(\Leftrightarrow x=\frac{\pi}{2}+k\pi\)
\(\frac{sin\left(2x+\frac{3\pi}{4}\right)}{c\text{os}\left(x+\frac{\pi}{4}\right)}+1=0\)
\(\cos\left(x+\frac{\pi}{3}\right)+\cos x=\frac{3}{2}-4\sin\left(\frac{x}{2}\right)\cdot\sin\left(\frac{x}{2}+\frac{\pi}{6}\right)\)
\(2\sin\left(\frac{\pi}{4}+x\right)+\sin\left(x-\frac{\pi}{4}\right)=\frac{3\sqrt{2}}{2}\)
\(2\sin\left(\frac{\pi}{4}+x\right)+\sin\left(x-\frac{\pi}{4}\right)=\frac{3\sqrt{2}}{2}\)
\(4sin\left(2x+\frac{3\pi}{5}\right)c\text{os}\left(2x+\frac{3\pi}{5}\right)-\sqrt{3}=0\)
Mọi người giúp em với, em cảm ơn ạ
Bài tập quy về dạng phương trình cơ bản:
\(1.\sin\left(x-\frac{\pi}{3}\right)+2cos\left(x-\frac{\pi}{6}\right)=0\);
\(2.\sin^23x=cos^2x\);
\(3.sin\left(2x-\frac{7\pi}{2}\right)+cos2x=1\)
\(4.\sqrt{2}cos\left(x-\frac{3\pi}{4}\right)=1+sinx\)
\(5.\sin\left(2x-\frac{7\pi}{2}\right)+cós2x=1\)
\(2\sin^2\left(5\pi+1\right)-\left(\sqrt{3}+1\right)\sin2\left(\frac{\pi}{2}-x\right)+\sqrt{3}\sin^2\left(\frac{9\pi}{2}+x\right)=0\)
\(\sqrt{3}sin\left(x+\frac{\pi}{4}\right)+cos\left(x+\frac{\pi}{4}\right)=1\)
Giải phương trình \(cos^4x+\sin^4x+cos\left(x-\frac{\pi}{4}\right)\times sin\left(3x-\frac{\pi}{4}\right)-\frac{3}{2}=0\)có nghiệm là:
A.\(x=\pm\frac{\pi}{4}+k2\pi\)
B.\(x=\frac{\pi}{2}+k\pi\)
C.\(x=\frac{\pi}{4}+k\pi\)
D.\(x=\frac{\pi}{4}+k2\pi\)