若1+sin^2=3sinacosa,求tana

若1+sin^2=3sinacosa,求tana
若1+sin^2=3sinacosa,求tana

若1+sin^2=3sinacosa,求tana
1+(sina)^2=3sina*cosa
(sina)^2+(cosa)^2+(sina)^2=3sina*cosa ( 用sina^2+cosa^2代换1）
2(tana)^2+1=3tan 等式两旁同除(cosa)^2
2(tana)^2-3tana+1=0
(2tana-1)(tana-1)=0
tana=1/2 or tana=1
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1=sin²a+cos²a
所以
sin²a+cos²a+sin²a=3sinacosa
2sin²a+cos²a=3sinacosa
两边同时除以cos²a得
2tan²a+1=3tana
2tan²a-3tana+1=0
(2tana-1)(tana-1)=0
tana=1/2或tana=1

1+sin^2=3sinacosa
sin^2a+cos^2a+sin^2a=3sinacosa
2sin^2a+cos^2a=3sinacosa
(2sin^2a+cos^2a)/sinacosa=3
2tana+1/tana=3
2tan^2a-3tana+1=0
(tana-1)(2tana-1)=0
tana=1或tana=1/2

1+sin^2=2sin^2a+cos^2a=3sinacosa两边同除以sinacosa得
=>2tana+1/tana=3
=>2tan^2a+1-3tana
=>tana=1或1/2

两边同时除以 cosA的平方
得到1/cos^2A + tan^2A = 3tanA
而1/cos^2A= 1+tan^2A
所以2tan^2A-3tanA+1=0
解得 tanA=1 或者 1/2