数学
三角函数计算 (22 18:57:20)计算:tan1°×tan2°×tan3°×tan4°×tan5°×……×tan87°×tan88°×tan89°

2019-05-27

三角函数计算 (22 18:57:20)
计算:tan1°×tan2°×tan3°×tan4°×tan5°×……×tan87°×tan88°×tan89°
优质解答
tan1°=tan(90°-89°)=ctan89°
tan2°=ctan88°
.
tan44°=ctan46°
tan45°=1
所以,
tan1°×tan2°×tan3°×tan4°×tan5°×……×tan87°×tan88°×tan89°
=tan89°×ctan89°×tan88°×ctan88°×...tan46°×ctan46°×tan45°
=1×1×1×...×1×1=1
tan1°=tan(90°-89°)=ctan89°
tan2°=ctan88°
.
tan44°=ctan46°
tan45°=1
所以,
tan1°×tan2°×tan3°×tan4°×tan5°×……×tan87°×tan88°×tan89°
=tan89°×ctan89°×tan88°×ctan88°×...tan46°×ctan46°×tan45°
=1×1×1×...×1×1=1
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