已知:tana-1/tana=-1,求1/[sina^2+2sina·cosa-(cos^2)·a]得值
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已知:tana-1/tana=-1,求1/[sina^2+2sina·cosa-(cos^2)·a]得值
![已知:tana-1/tana=-1,求1/[sina^2+2sina·cosa-(cos^2)·a]得值](/uploads/image/z/7815152-56-2.jpg?t=%E5%B7%B2%E7%9F%A5%3Atana-1%2Ftana%3D-1%2C%E6%B1%821%2F%5Bsina%5E2%2B2sina%C2%B7cosa-%28cos%5E2%29%C2%B7a%5D%E5%BE%97%E5%80%BC)
sina/cosa-cosa/sina=-1
(sin^2a-cos^2a)/sinacosa=-1
sin^2a-cos^2a=-sinacosa
1/[sina^2+2sina·cosa-(cos^2)·a]
=1/sinacosa
=sin^2a+cos^2a/sinacosa
=sina/cosa+cosa/sina
=tana+1/tana
tana-1/tana=-1
tan^2a+1/tan^2a-2=-1
tan^2a+1/tan^2a=1
(tana+1/tana)^2=3
tana+1/tana=+-根号3
(sin^2a-cos^2a)/sinacosa=-1
sin^2a-cos^2a=-sinacosa
1/[sina^2+2sina·cosa-(cos^2)·a]
=1/sinacosa
=sin^2a+cos^2a/sinacosa
=sina/cosa+cosa/sina
=tana+1/tana
tana-1/tana=-1
tan^2a+1/tan^2a-2=-1
tan^2a+1/tan^2a=1
(tana+1/tana)^2=3
tana+1/tana=+-根号3
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