化简下列各式,(1+tan2α)cos2α1.(1+tan²α)cos²α2.sin50°(1+√3tan10°)有图!

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化简下列各式,(1+tan2α)cos2α1.(1+tan²α)cos²α2.sin50°(1+√3tan10°)有图!
化简下列各式,(1+tan2α)cos2α
1.(1+tan²α)cos²α
2.sin50°(1+√3tan10°)
有图!

化简下列各式,(1+tan2α)cos2α1.(1+tan²α)cos²α2.sin50°(1+√3tan10°)有图!
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1.
(1+tan²α)cos²α
=[1 + (sin²α/cos²α)]·cos²α
=[(sin²α+cos²α)/cos²α]·cos²α
=1
2.
1+√3tan10°
=1+(√3sin10°/cos10°)
=(cos10°+√3sin10°)/cos10°
=2[(1/2)cos10°+(√3/2)sin10°]/cos10°
=2[sin30°cos10°+cos30°sin10°]/cos10°
=2sin(30°+10°)/cos10°
=2sin40°/cos10°
sin50°(1+√3tan10°)
=(2sin40°sin50°)/cos10°
=(2sin40°cos40°)/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1