Bài tập 45 trang 47 SGK Toán 11 NC

Bài tập 45 trang 47 SGK Toán 11 NC

a)

\(\begin{array}{l}
\sin x + \tan \frac{\pi }{7}\cos x = \sin x + \frac{{\sin \frac{\pi }{7}}}{{\cos \frac{\pi }{7}}}\cos x\\
 = \frac{1}{{\cos \frac{\pi }{7}}}\left( {\sin x\cos \frac{\pi }{7} + \sin \frac{\pi }{7}\cos \frac{\pi }{7}} \right)\\
 = \frac{1}{{\cos \frac{\pi }{7}}}\sin \left( {x + \frac{\pi }{7}} \right)
\end{array}\)

b)

\(\begin{array}{l}
\tan \frac{\pi }{7}\sin x + \cos x = \frac{{\sin \frac{\pi }{7}}}{{\cos \frac{\pi }{7}}}\sin x + \cos x\\
 = \frac{1}{{\cos \frac{\pi }{7}}}\left( {\sin x\sin \frac{\pi }{7} + \cos x\cos \frac{\pi }{7}} \right)\\
 = \frac{1}{{\cos \frac{\pi }{7}}}\cos \left( {x - \frac{\pi }{7}} \right) = \frac{1}{{\cos \frac{\pi }{7}}}\sin \left( {x - \frac{\pi }{7} + \frac{\pi }{2}} \right)
\end{array}\)

-- Mod Toán 11