计算:(sin65°+sin15°sin10°)/(sin25°-cos15°cos80°)的值为?
问题描述:
计算:(sin65°+sin15°sin10°)/(sin25°-cos15°cos80°)的值为?
答
原式
=[sin(90°-25°)+sin15°sin10°]/[sin(15°+10°)-cos15°cos(90°-10°)]
=(cos25°+sin15°sin10°)/(sin15°cos10°+cos15°sin10°-cos15°sin10°)
=[cos(15°+10°)+sin15°sin10°]/sin15°cos10
=(cos15°cos10°-sin15°sin10°+sin15°sin10°)/sin15°cos10
=cos15°/sin15°
=cot15°
=tan75°
=2+√3