Question

Giải phương trình: \(\sin\left(\frac{3\pi}{10}-\frac{x}{2}\right)=\frac{1}{2}\sin\left(\frac{\pi}{10}+\frac{3x}{2}\right)\)

Answer 1

Đặt \(\frac{3\pi}{10}-\frac{x}{2}=a\Rightarrow\frac{x}{2}=\frac{3\pi}{10}-a\Rightarrow\frac{3x}{2}=\frac{9\pi}{10}-3a\)

Phương trình trở thành:

\(sina=\frac{1}{2}sin\left(\frac{\pi}{10}+\frac{9\pi}{10}-3a\right)\)

\(\Leftrightarrow2sina=sin\left(\pi-3a\right)=sin3x\)

\(\Leftrightarrow2sina=3sina-4sin^3a\)

\(\Leftrightarrow4sin^3a-sina=0\)

\(\Leftrightarrow sina\left(2sina-1\right)\left(2sina+1\right)=0\)

\(\Leftrightarrow...\)