Question

Biết rằng \(sin\left(x-\frac{\pi}{3}\right)+sin\frac{13\pi}{2}=sin\left(x+\frac{\pi}{3}\right)\). Tính gtri của \(cosx\)

Answer 1

\(sin\left(x+\frac{\pi}{3}\right)-sin\left(x-\frac{\pi}{3}\right)=sin\left(6\pi+\frac{\pi}{2}\right)\)

\(\Leftrightarrow2cosx.sin\frac{\pi}{3}=sin\left(\frac{\pi}{2}\right)\)

\(\Leftrightarrow2cosx.\frac{\sqrt{3}}{2}=1\)

\(\Rightarrow cosx=\frac{1}{\sqrt{3}}\)