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    【题目】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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