若tanα=3,求sin2α-cos2α的值

若tanα=3,求sin2α-cos2α的值
若tanα=3,求sin2α-cos2α的值

若tanα=3,求sin2α-cos2α的值
tanα=sinα/cosα=3
sinα=3cosα
sin²α+cos²α=1
9cos²α+cos²α=1
10cos²α=1
cos²α=1/10
sin2α-cos2α
=2sinαcosα-cos²α+sin²α
=cos²α(2tanα-1+tan²α)
=(1/10)(2×3-1+3²)
=7/5

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