4cos50°-tan40°怎么求啊?
1个回答

4cos50-tan40

=4sin40-sin40/cos40

=(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