计算cosπ/3-tanπ/4+3/4tan²π/6-sinπ/6+cos²π/6
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计算cosπ/3-tanπ/4+3/4tan²π/6-sinπ/6+cos²π/6
cosπ/3-tanπ/4+3/4tan²π/6-sinπ/6+cos²π/6
[tan(-150°)cos(-210°)cos420°]/cot(-600°)sin(-1050°)
cos25/6π+cos25/3π+tan(-25/4π)
5sinπ/2+2cos0-3sin3/2π+10cosπ
tan10°tan20°tan30°tan45°tan60°tan70°tan80°
过程要详细
cosπ/3-tanπ/4+3/4tan²π/6-sinπ/6+cos²π/6
[tan(-150°)cos(-210°)cos420°]/cot(-600°)sin(-1050°)
cos25/6π+cos25/3π+tan(-25/4π)
5sinπ/2+2cos0-3sin3/2π+10cosπ
tan10°tan20°tan30°tan45°tan60°tan70°tan80°
过程要详细
![计算cosπ/3-tanπ/4+3/4tan²π/6-sinπ/6+cos²π/6](/uploads/image/z/19108527-15-7.jpg?t=%E8%AE%A1%E7%AE%97cos%CF%80%2F3-tan%CF%80%2F4%2B3%2F4tan%26%23178%3B%CF%80%2F6-sin%CF%80%2F6%2Bcos%26%23178%3B%CF%80%2F6)
答:
1)
cosπ/3-tanπ/4+3/4tan²π/6-sinπ/6+cos²π/6
=1/2-1+(3/4)*(√3/3)²-1/2+(√3/2)²
=-1+(3/4)*(1/3)+3/4
=-1+1/4+3/4
=0
2)
[tan(-150°)cos(-210°)cos420°]/cot(-600°)sin(-1050°)
=(tan30°cos210°cos60°) / [cot(-60°)sin(-30°)]
=( -tan30°cos30°cos60°) / (cot60°sin30°)
=-sin30°cos60°tan60°/sin30°
=-sin60°
=-√3/2
3)
cos25/6π+cos25/3π+tan(-25/4π)
=cos(π/6)+cos(π/3)-tan(π/4)
=√3/2+1/2-1
=(√3-1)/2
4)
5sinπ/2+2cos0-3sin3/2π+10cosπ
=5*1+2-3*(-1)+10*(-1)
=5+2+3-10
=0
5)
tan10°tan20°tan30°tan45°tan60°tan70°tan80°
=tan10°tan20°tan30°tan45°ctan30°ctan20°ctan10°
=(tan10°ctan10°)*(tan20°ctan20°)*(tan30°ctan30°)tan45°
=1×1×1×1
=1
1)
cosπ/3-tanπ/4+3/4tan²π/6-sinπ/6+cos²π/6
=1/2-1+(3/4)*(√3/3)²-1/2+(√3/2)²
=-1+(3/4)*(1/3)+3/4
=-1+1/4+3/4
=0
2)
[tan(-150°)cos(-210°)cos420°]/cot(-600°)sin(-1050°)
=(tan30°cos210°cos60°) / [cot(-60°)sin(-30°)]
=( -tan30°cos30°cos60°) / (cot60°sin30°)
=-sin30°cos60°tan60°/sin30°
=-sin60°
=-√3/2
3)
cos25/6π+cos25/3π+tan(-25/4π)
=cos(π/6)+cos(π/3)-tan(π/4)
=√3/2+1/2-1
=(√3-1)/2
4)
5sinπ/2+2cos0-3sin3/2π+10cosπ
=5*1+2-3*(-1)+10*(-1)
=5+2+3-10
=0
5)
tan10°tan20°tan30°tan45°tan60°tan70°tan80°
=tan10°tan20°tan30°tan45°ctan30°ctan20°ctan10°
=(tan10°ctan10°)*(tan20°ctan20°)*(tan30°ctan30°)tan45°
=1×1×1×1
=1
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