若tanα=3,求sin2α-cos2α的值

數(shù)學(xué)人氣：643 ℃時(shí)間：2020-04-14 07:25:48

優(yōu)質(zhì)解答

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)
=7/52sinαcosα-cos²α+sin²α=cos²α(2tanα-1+tan²α)不明白2sinacosa-cos^2a+sin^2a=（2sinacosa-cos^2a+sin^2a)/1分子分母同時(shí)除以cos^a=(2tana-1+tan^2a)/ (1/cos^2a)=cos²α(2tanα-1+tan²α)實(shí)際上就是提取cos^2a