Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
17,\\
\sin 200^\circ .\sin 310^\circ + \cos 340^\circ .\cos 50^\circ \\
= \sin \left( {180^\circ - 200^\circ } \right).\sin \left( { - 50^\circ + 360^\circ } \right) + \cos \left( { - 20^\circ + 360^\circ } \right).\cos 50^\circ \\
= \sin \left( { - 20^\circ } \right).\sin \left( { - 50^\circ } \right) + \cos \left( { - 20^\circ } \right).cos50^\circ \\
= - \sin 20^\circ .\left( { - \sin 50^\circ } \right) + \cos 20^\circ .\cos 50^\circ \\
= \cos 20^\circ .\cos 50^\circ + \sin 20^\circ .\sin 50^\circ \\
= \cos \left( {50^\circ - 20^\circ } \right)\\
= \cos 30^\circ \\
= \frac{{\sqrt 3 }}{2}\\
18,\\
2\cos x.\cos y = \cos \left( {x + y} \right) + \cos \left( {x - y} \right)\\
4\cos 15^\circ .\cos 21^\circ .\cos 24^\circ - \cos 12^\circ - \cos 18^\circ \\
= 2.\left( {2\cos 15^\circ .\cos 21^\circ } \right).\cos 24^\circ - \cos 12^\circ - \cos 18^\circ \\
= 2.\left( {\cos 36^\circ + \cos 6^\circ } \right).cos24^\circ - \cos 12^\circ - \cos 18^\circ \\
= 2\cos 36^\circ .\cos 24^\circ + 2\cos 6^\circ .\cos 24^\circ - \cos 12^\circ - \cos 18^\circ \\
= \left( {\cos 60^\circ + \cos 12^\circ } \right) + \left( {\cos 30^\circ + \cos 18^\circ } \right) - \cos 12^\circ - \cos 18^\circ \\
= \cos 60^\circ + \cos 30^\circ \\
= \frac{{1 + \sqrt 3 }}{2}
\end{array}\)
