4倍的50度的余弦值减去40度的正切值等于多少
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4cos50º-tan40º
=4sin40º-sin40º/cos40º
=(4sin40°cos40°-sin40°)/cos40°
=(2sin80°-sin40°)/cos40°
=[2cos10°-sin(30°+10°)]/cos40°
=(2cos10°-1/2cos30°-√3/2sin10°)/cos40°
=(3/2cos10°-√3/2sin10°)/cos40°
=√3(√3/2cos10°-1/2sin10°)/cos40°
=√3(cos30°cos10°-sin30°sin10°)/cos40°
=√3cos40°/cos40°
=√3
=4sin40º-sin40º/cos40º
=(4sin40°cos40°-sin40°)/cos40°
=(2sin80°-sin40°)/cos40°
=[2cos10°-sin(30°+10°)]/cos40°
=(2cos10°-1/2cos30°-√3/2sin10°)/cos40°
=(3/2cos10°-√3/2sin10°)/cos40°
=√3(√3/2cos10°-1/2sin10°)/cos40°
=√3(cos30°cos10°-sin30°sin10°)/cos40°
=√3cos40°/cos40°
=√3
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