求(sin15°-cos15°)/(sin15°+cos15°)的值

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求(sin15°-cos15°)/(sin15°+cos15°)的值

求(sin15°-cos15°)/(sin15°+cos15°)的值
求(sin15°-cos15°)/(sin15°+cos15°)的值

求(sin15°-cos15°)/(sin15°+cos15°)的值
分子分母同时乘以sin15°-cos15°
原式
=(sin15°-cos15°)/(sin15°+cos15°)
=(sin15°-cos15°)²/(sin²15°-cos15²°)
=(sin²15°-2*sin15°cos15°+cos²15°)/(-cos(2*15°))
=(1-sin30°)/(-cos30°)
=(1-1/2)/(-√3/2)
=-√3/3