【題目】求下列各式的值.
（1）sin 195°＋cos 105°；
（2）cos（α－45°）cos（15°＋α）＋cos（α＋45°）cos（105°＋α）.
【答案】（1）
（2）
【解析】（1）原式＝cos 105°＋sin 195°
＝cos 105°＋sin（90°＋105°）
＝cos 105°＋cos 105°
＝2cos 105°＝2cos（135°－30°）
＝2×（cos 135°cos 30°＋sin 135°sin 30°）
＝2×
（2）原式＝cos（α－45°）cos（15°＋α）＋sin（45°－α）cos（15°＋90°＋α）
＝cos（α－45°）cos（15°＋α）－sin（45°－α）sin（15°＋α）
＝cos（α－45°）cos（15°＋α）＋sin（α－45°）sin（15°＋α）
＝cos[（α－45°）－（15°＋α）]
＝cos（－60°）＝cos 60°＝
.
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