sin(540°+α)cos(360°-α)/sin(450°+α)tan(900°-α) 急!

sin(540°+α)cos(360°-α)/sin(450°+α)tan(900°-α) 急!

sin(540°+α)cos(360°-α)/[sin(450°+α)tan(900°-α)]
=sin(180°+α)cosα/[sin(90°+α)tan(180°-α)]
=-sinαcosα/[-cosα.tanα]
=-sinαcosα/[-sinα]
=cosα

化簡cos(α -π )tan(α-2π)tan(2π-α)/sin(π+α)

cos(α -π )tan(α-2π)tan(2π-α)/sin(π+α)
=[-cos(α)]tan(α)[-tan(α)]/[-sin(α)]
=tan(α)[-tan(α)]/[tan(α)]
= -tan(α)

化簡 sin平方（派-α）+tan（-α）分之sin（-α）cos（2派-α）

化簡 sin平方（派-α）+tan（-α）分之sin（-α）cos（2派-α）
=sin²α+sinα*cosα/tanα
=sin²α+cos²α=1

cos^2α-sin^2α/cos^2α+sin^2α=1-tan^2α/1+tan^2α 那個表示平方,請問如何化簡

分子分母同時除以cosa^2
cos^2α-sin^2α/cos^2α+sin^2α
=1-tana^2/1+tana^2

tanα=-2,則sin平方α+sinαcosα=?

(sina)²+sinacosa
=sin²a+sinacosa
=(sin²a+sinacosa)/(sin²a+cos²a)
=(tan²a+tana)/(tan²a+1)
=(2²+2)/(2²+1)
=6/5
=5分之6

tan(π-α)*sin^2(α+π/2)*cos(2π-α)/cos^3(-α-π)*tan(2π-α) sin^2就是sin的平方,下同

tan(π-α)=-tanα
sin(α+π/2)=-cosα
cos(2π-α)=cosα
cos(-α-π)=-cosα
tan(2π-α)=--tanα
代入=-1

tanα=2,（sinα+cosα）的平方得多少,過程

用asina/cosa=tana=2sina=2cosasi²a=4cos²a因為sin²a+cos²a=1所以cos²a=1/5所以原式=sin²a+cos²a+2sinacosa=1+2(2cosa)cosa=1+4cos²a=9/5

求證：tan a/2＝(1-cos)/sin a=sin a/(cos a+1)

cos(a/2)不等於0.
tan(a/2) = sin(a/2)/cos(a/2) = 2sin(a/2)cos(a/2)/{2[cos(a/2)]^2}
= sin(a)/[1 + cos(a)]
當 sin(a/2)不等於0時,
tan(a/2) = sin(a/2)/cos(a/2) = 2[sin(a/2)]^2/[2sin(a/2)cos(a/2)]
= [1 - cos(a)]/sin(a)

求證：（1-sinα+cosα）/（1+sinα+cosα）=tan(π/4-α/2)

證明：（1-sinα+cosα）/（1+sinα+cosα）=[sin^2(a/2)+cos^2(a/2)-2sina/2cosa/2+cos^2（a/2）-sin^2(a/2）]/[sin^2(a/2)+cos^2(a/2)+2sina/2cosa//2+cos^2（a/2）-sin^2(a/2）]=[2cos^2(a/2)-2sina/2cosa/2]/[2c...

求證(1+sinα/1-sinα)=(1/cosα+tanα)^2

證明：左邊=1+sinα/1-sinα
右邊=(1/cosα+tanα)^2
=(1/cosα+sinα/cosα)^2
=(1+sinα/cosα) ^2
=(1+sinα) ^2/(cosα)^2
=(1+sinα) ^2/1-(sinα)^2
=(1+sinα) ^2/(1+sinα)(1-sinα)
=1+sinα/1-sinα
=左邊
即證.