Bài 1.7 trang 21 SGK Toán 11 tập 1 - Kết nối tri thức

\(\cos {15^0} = \cos \left( {{{45}^0} - {{30}^0}} \right)\)

\(= \cos {45^0}\cos {30^0} + \sin {45^0}\sin {30^0}\)

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

\(= \frac{{\sqrt 6  + \sqrt 2 }}{4}\).

\(\sin {15^0} = \sin \left( {{{45}^0} - {{30}^0}} \right) \)

\(= \sin {45^0}\cos {30^0} - \cos {45^0}\sin {30^0} \)

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

\(= \frac{{\sqrt 6  - \sqrt 2 }}{4}\).

\(\tan {15^0} = \tan \left( {{{45}^0} - {{30}^0}} \right) \)

\(= \frac{{\tan {{45}^0} - \tan {{30}^0}}}{{1 + \tan {{45}^0}\tan {{30}^0}}} \)

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

\(\cot {15^0} = \frac{1}{{\tan {{15}^0}}} = \frac{1}{{2 - \sqrt 3 }}\).