Question

Giải phương trình: \(2cos\left(x+\frac{\pi}{6}\right)+3cos\left(x-\frac{\pi}{3}\right)=\frac{5\sqrt{2}}{2}\)

Answer 1

\(\Leftrightarrow2sin\left(\frac{\pi}{3}-x\right)+3cos\left(\frac{\pi}{3}-x\right)=\frac{5\sqrt{2}}{2}\)

\(\Leftrightarrow\frac{2}{\sqrt{13}}sin\left(\frac{\pi}{3}-x\right)+3cos\left(\frac{\pi}{3}-x\right)=\frac{5\sqrt{26}}{26}\)

Đặt \(\frac{2}{\sqrt{13}}=cosa\) với \(a\in\left(0;\pi\right)\)

\(\Rightarrow sin\left(\frac{\pi}{3}-x\right)cosa+cos\left(\frac{\pi}{3}-x\right)sina=\frac{5\sqrt{26}}{26}\)

\(\Leftrightarrow sin\left(\frac{\pi}{3}-x+a\right)=\frac{5\sqrt{26}}{26}\)

\(\Leftrightarrow...\)