Tính: \(\sin \frac{\pi }{8},\cos \frac{\pi }{8}\).

Áp dụng công thức hạ bậc, ta có:

• \({\sin ^2}\frac{\pi }{8} = \frac{{1 - cos\left( {2.\frac{\pi }{8}} \right)}}{2} = \frac{{1 - \cos \frac{\pi }{4}}}{2} = \frac{{1 - \frac{{\sqrt 2 }}{2}}}{2} = \frac{{2 - \sqrt 2 }}{4}\)

Mà \(\sin \frac{\pi }{8} > 0\) nên \(\sin \frac{\pi }{8} = \sqrt {\frac{{2 - \sqrt 2 }}{4}} = \frac{{\sqrt {2 - \sqrt 2 } }}{2}\).

• \({\cos ^2}\frac{\pi }{8} = \frac{{1 + cos\left( {2.\frac{\pi }{8}} \right)}}{2} = \frac{{1 + \cos \frac{\pi }{4}}}{2} = \frac{{1 + \frac{{\sqrt 2 }}{2}}}{2} = \frac{{2 + \sqrt 2 }}{4}\)

Mà \(\cos \frac{\pi }{8} > 0\) nên \(\cos \frac{\pi }{8} = \sqrt {\frac{{2 + \sqrt 2 }}{4}} = \frac{{\sqrt {2 + \sqrt 2 } }}{2}\).