Evaluation: 4sin40 ° - tan40 °

Evaluation: 4sin40 ° - tan40 °

4sin40-tan40
=(4sin40cos40-sin40)/cos40
=(2sin80-sin40)/cos40
=(2cos10-sin40)/cos40
=[2cos10-sin(30+10)]/cos40
=[2cos10-1/2*cos10-√3/2*sin10]/cos40
=(3/2*cos10-√3/2*sin10)/cos40
=√3*(√3/2*cos10-1/2*sin10)/cos40
=√3*(cos30*cos10-sin30sin10)/cos40
=√3*cos40/cos40
=√3
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4sin40+tan40=?

4sin40-tan40=(4sin40cos40-sin40)/cos40=(2sin80-sin40)/cos40=(2cos10-sin40)/cos40=[2cos10-sin(30+10)]/cos40=[2cos10-1/2*cos10-√3/2*sin10]/cos40=(3/2*cos10-√3/2*sin10)/cos40=√3*(√3/2*cos10-1/2*sin10...

tan40-4sin40

tan40-4sin40
sin40
= ----- -4sin40
cos40
sin40-4sin40cos40
= -------------------
cos40
sin40-2sin80
= --------------
cos40
sin40-sin80-sin80
= ------------------
cos40
2cos60sin(-20)-sin80
= ---------------------
cos40
sin80+sin20
= － -----------
cos40
2sin50cos30
= － -----------
cos40
=Negative radical 3