Question

三角函数的化简

1.（1+tan²α）cos²α

2.sin50°（1+√3tan10°）

要具体过程！有加分！谢谢

Answer 1

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