sin15°-cos15°/sin15°+cos15°的值?
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/26 01:57:50
sin15°-cos15°/sin15°+cos15°的值?
设sin15°-cos15°/sin15°+cos15°=X
则(sin15°-cos15°/sin15°+cos15°)²
=(sin15°-cos15°)²/(sin15°+cos15°)²
=(sin²15°+cos²15°-2sin15°cos15°)/(sin²15°+cos²15°+2sin15°cos15°)
=(1-sin30°)/(1+sin30°)
=1/2 / 3/2=1/3 即X²=1/3 X=√3/3
所以sin15°-cos15°/sin15°+cos15°=√3/3
则(sin15°-cos15°/sin15°+cos15°)²
=(sin15°-cos15°)²/(sin15°+cos15°)²
=(sin²15°+cos²15°-2sin15°cos15°)/(sin²15°+cos²15°+2sin15°cos15°)
=(1-sin30°)/(1+sin30°)
=1/2 / 3/2=1/3 即X²=1/3 X=√3/3
所以sin15°-cos15°/sin15°+cos15°=√3/3
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