Question

根号3/cos10°-1/cos80°=?

Answer 1

√3/cos10°-1/cos80°
=√3/sin80°-1/cos80°
=(√3cos80°-sin80°)/sin80°cos80°
=2(√3/2*cos80°-1/2*sin80°)/(1/2*sin160°)
=4cos(30°+80°)/sin160°
=4cos110°/sin20°
=-4cos70°/cos70°
=-4

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Answer 2

1/cos80度-根号3/cos10度
=1/sin10-根号3/cos10
=(cos10-根号3sin10)/(sin10*cos10)
=2(cos10*cos60-sin60*sin10)/(sin20°/2)
=2cos70/(sin20°/2)
=4

所以 根号3/cos10°-1/cos80° = -4

Answer 3

√3/cos10°-1/cos80°=√3/cos10°-1/sin10°=(√3sin10°-cos10°)/sin10°cos10°
=2(√3/2sin10°-1/2cos10°)/sin10°cos10=2(sin10°cos30°-sin30°cos10°)/sin10°cos10°
=-4sin20°/sin20°=-4