sina+[sina/√(1-sin^2a)]=1怎么解 高分?
2个回答

郭敦顒回答:

∵sina+[sina/√(1-sin^2a)]=1

∴ [sina/√(1-sin^2a)]=1-sina,

两边平方得,sin²a/(1-sin²a)=1-2sina+sin²a,

sin²a=(1+sin²a)(1-sin²a) -2sina(1-sin²a),

sin²a=(1-sin^4a) -2sina+2sin³a,

sin^4a-2sin³a + sin²a+2sina-1=0,

解这个4次方程得,

sina≈0.4689899435,

∠A=27.9687515°;

∵(1-sin^2a)= cos²a,∴[sina/√(1-sin^2a)]= sina/cosa= tana,

∴sina+ tana=1,

用尝试——逐步逼近法解得,

sina≈0.4689899435,tana≈0 .5310100565,

∠A=27.9687515°.