若sin^2α-sin2α-3cos^2α=0,则tanα=?

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若sin^2α-sin2α-3cos^2α=0,则tanα=?

若sin^2α-sin2α-3cos^2α=0,则tanα=?
若sin^2α-sin2α-3cos^2α=0,则tanα=?

若sin^2α-sin2α-3cos^2α=0,则tanα=?
sin^2α-sin2α-3cos^2α=0
sin^2α-2sinαcosα-3cos^2α=0
两边同时除以cos^2α,得:
tan^2α-2tanα-3=0
(tanα+1)(tanα-3)=0
tanα=-1或3

sin^2α-sin2α-3cos^2α=0
sin^2α-2sinαcosα-3cos^2α=0
(sinα-3cosα)(sinα+cosα)=0
sinα=3cosα,sinα=-cosα
所以tanα=sinα/cosα=3或-1