Bài tập 44 trang 214 SGK Toán 10 NC

a) Ta có

\(\begin{array}{l}
\sin \left( {\frac{\pi }{3} + \alpha } \right) - \sin \left( {\frac{\pi }{3} - \alpha } \right)\\
 = 2\cos \frac{\pi }{3}\sin \alpha  = \sin \alpha 
\end{array}\)

b)

\(\begin{array}{l}
{\cos ^2}\left( {\frac{\pi }{4} + \alpha } \right) - {\cos ^2}\left( {\frac{\pi }{4} - \alpha } \right)\\
 = \frac{{1 + \cos \left( {\frac{\pi }{2} + 2\alpha } \right)}}{2} - \frac{{1 + \cos \left( {\frac{\pi }{2} - 2\alpha } \right)}}{2}\\
 = \frac{1}{2}\left( { - \sin 2\alpha  - \sin 2\alpha } \right) =  - \sin 2\alpha 
\end{array}\)

-- Mod Toán 10 HỌC247