已知sinα+coaα=√2/2,1/sinα^2+1/cosα^2已知sinα+coaα=√2/2,求1/sinα^2+1/cosα^2 已知tanα=-1/2,求sinα^2+2sinαcosα-3cosα^2求证:1/2sinαcoaα / sinα^2-cosα^2 = tanα+1 / tanα-1
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![已知sinα+coaα=√2/2,1/sinα^2+1/cosα^2已知sinα+coaα=√2/2,求1/sinα^2+1/cosα^2 已知tanα=-1/2,求sinα^2+2sinαcosα-3cosα^2求证:1/2sinαcoaα / sinα^2-cosα^2 = tanα+1 / tanα-1](/uploads/image/z/3010135-31-5.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B1%2Bcoa%CE%B1%3D%E2%88%9A2%2F2%2C1%2Fsin%CE%B1%5E2%2B1%2Fcos%CE%B1%5E2%E5%B7%B2%E7%9F%A5sin%CE%B1%2Bcoa%CE%B1%3D%E2%88%9A2%2F2%2C%E6%B1%821%2Fsin%CE%B1%5E2%2B1%2Fcos%CE%B1%5E2+%E5%B7%B2%E7%9F%A5tan%CE%B1%3D-1%2F2%EF%BC%8C%E6%B1%82sin%CE%B1%5E2%2B2sin%CE%B1cos%CE%B1-3cos%CE%B1%5E2%E6%B1%82%E8%AF%81%EF%BC%9A1%2F2sin%CE%B1coa%CE%B1+%2F+sin%CE%B1%5E2-cos%CE%B1%5E2+%3D+tan%CE%B1%2B1+%2F+tan%CE%B1-1)
已知sinα+coaα=√2/2,1/sinα^2+1/cosα^2已知sinα+coaα=√2/2,求1/sinα^2+1/cosα^2 已知tanα=-1/2,求sinα^2+2sinαcosα-3cosα^2求证:1/2sinαcoaα / sinα^2-cosα^2 = tanα+1 / tanα-1
已知sinα+coaα=√2/2,1/sinα^2+1/cosα^2
已知sinα+coaα=√2/2,求1/sinα^2+1/cosα^2
已知tanα=-1/2,求sinα^2+2sinαcosα-3cosα^2
求证:1/2sinαcoaα / sinα^2-cosα^2 = tanα+1 / tanα-1
已知sinα+coaα=√2/2,1/sinα^2+1/cosα^2已知sinα+coaα=√2/2,求1/sinα^2+1/cosα^2 已知tanα=-1/2,求sinα^2+2sinαcosα-3cosα^2求证:1/2sinαcoaα / sinα^2-cosα^2 = tanα+1 / tanα-1
1,sinα+coaα=√2/2
(sinα+coaα)^2=1/2
1+2sinαcosα=1/2
sinαcosα=-1/4
(sinαcosα)^2=1/16
1/sinα^2+1/cosα^2
=1/((sinαcosα)^2)=16
2,已知tanα=-1/2,求sinα^2+2sinαcosα-3cosα^2
sinα^2+2sinαcosα-3cosα^2
=(sinα^2+2sinαcosα-3cosα^2)/(sinα^2+cosα^2)
=(tanα^2+2tanα-3)/(tanα^2+1)
=(1/4-1-3)/(1/4+1)
=(-15/4)/(5/4)
=-3
3,求证:1-2sinαcoaα / sinα^2-cosα^2 = tanα+1 / tanα-1
∵cosa^2+sina^2=1,
∴左边=-[cosa^2+sina^2-2sina*cosa/cos^2-sin^2]
=-(cosa-sina)^2/cos^2-sin^2
上下同除cosa-sina
原式=-(cosa-sina)/cosa+sina
上下同除cosa
原式=(tana-1)/(1+tana)
sinα+coaα=√2/2
sin²α+2sinacosa+coa²α=1/2
1+2sinacosa=1/2
sinacosa=-1/4
1/sinα^2+1/cosα^2
=1/[sin²acos²a]
=16
1/sinα^2+1/cosα^2 =1/[(sina)^2(cosa)^2]即[1/sinacosa]^2
再将sinα+coaα=√2/2两边平方得
1+2sinacosa=1/2得sinacosa=-(1/4)
则[1/sinacosa]^2=16
16