临海市现任领导班子:化简:2sin50°/sin100°+tan10°

来源:百度文库 编辑:查人人中国名人网 时间:2024/05/05 09:41:22
这是一道高一年级的关于三角函数的化简题!

2sin50°/sin100°+tan10°
=2sin50°/cos10°+sin10°/cos10°
=(2sin50°+sin10°)/cos10°
=[2sin(60°-10°)+sin10°]/cos10°
=(√3cos10°-sin10°+sin10°)/cos10°
=√3

2sin50°/sin100°+tan10°
=2sin50°/cos10°+sin10°/cos10°
=(2sin50°+sin10°)/cos10°
=[2sin(60°-10°)+sin10°]/cos10°
=(√3cos10°-sin10°+sin10°)/cos10°
=√3

原式=2sin50/cos10+sin10/cos10
=[2sin60cos10-2cos60sin10+sin10]/cos10
=√3

=2sin50/cos10+sin10/cos10
=[2sin60cos10-2cos60sin10+sin10]/cos10
=√3