Question

若tanα=3，求sin2α-cos2α的值

Answer 1

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

追问

2sinαcosα-cos²α+sin²α
=cos²α(2tanα-1+tan²α)不明白

追答

2sinacosa-cos^2a+sin^2a
=（2sinacosa-cos^2a+sin^2a)/1
分子分母同时除以cos^a
=(2tana-1+tan^2a)/ (1/cos^2a)
=cos²α(2tanα-1+tan²α)
实际上就是提取cos^2a

Answer 2

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