1.secx=1/cosx cscx=1/sinx
1/sin10°-√3/cos10°=(cos10°-√3sin10°)/sin10°*cos10°
=2sin(30°-10°)/sin10°*cos10°=2sin20°/sin10°*cos10°=4
2.cos40°×（1＋√3cot80)
=cos40°*(sin80°+√3cos80°)/sin80°
=cos40°*2sin(80°+60°)/sin80°
=2cos40°sin40°/sin80°
=sin80°/sin80°
=1
3.tan70cos10(√3sin20-cos20)/cos20
=tan70cos10*2sin(20-30)/cos20
=-tan70sin20/cos20
=-sin(90-20)/cos(90-20) *tan20
=1/tan20*tan20
=1
4.
cos4(π/8)+cos4(3π/8)+cos4(π/8-4π/8)+cos4(3π/8-4π/8)
=cos4(π/8)+cos4(3π/8)+sin4(π/8)+sin4(3π/8)
=[sin2(π/8)+cos2(π/8)]^2+[sin2(3π/8)+cos2(3π/8)]^2-2sin2(π/8)cos2(π/8)-2sin2(3π/8)cos2(3π/8)
=2-1/2[4sin2(π/8)cos2(π/8)+4sin2(3π/8)cos2(3π/8)]
=2-1/2[sin2(π/4)+sin2(3π/4)]
=2-1/2[sin2(π/4)+sin2(π/4)]
=2-1/2=3/2
5.
第5题同上,你自己算吧 算这题太累了. 1.secx=1/cosx cscx=1/sinx
1/sin10°-√3/cos10°=(cos10°-√3sin10°)/sin10°*cos10°
=2sin(30°-10°)/sin10°*cos10°=2sin20°/sin10°*cos10°=4
2.cos40°×（1＋√3cot80)
=cos40°*(sin80°+√3cos80°)/sin80°
=cos40°*2sin(80°+60°)/sin80°
=2cos40°sin40°/sin80°
=sin80°/sin80°
=1
3.tan70cos10(√3sin20-cos20)/cos20
=tan70cos10*2sin(20-30)/cos20
=-tan70sin20/cos20
=-sin(90-20)/cos(90-20) *tan20
=1/tan20*tan20
=1
4.
cos4(π/8)+cos4(3π/8)+cos4(π/8-4π/8)+cos4(3π/8-4π/8)
=cos4(π/8)+cos4(3π/8)+sin4(π/8)+sin4(3π/8)
=[sin2(π/8)+cos2(π/8)]^2+[sin2(3π/8)+cos2(3π/8)]^2-2sin2(π/8)cos2(π/8)-2sin2(3π/8)cos2(3π/8)
=2-1/2[4sin2(π/8)cos2(π/8)+4sin2(3π/8)cos2(3π/8)]
=2-1/2[sin2(π/4)+sin2(3π/4)]
=2-1/2[sin2(π/4)+sin2(π/4)]
=2-1/2=3/2
5.
第5题同上,你自己算吧 算这题太累了.