已知2sinαtanα=3,则sin^4-cos^4的值是

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已知2sinαtanα=3,则sin^4-cos^4的值是已知2sinαtanα=3,则sin^4-cos^4的值是已知2sinαtanα=3,则sin^4-cos^4的值是由2sinαtanα=3得

已知2sinαtanα=3,则sin^4-cos^4的值是
已知2sinαtanα=3,则sin^4-cos^4的值是

已知2sinαtanα=3,则sin^4-cos^4的值是
由2sinαtanα=3得:(sinα)^2=(3/2)cosα=1-(cosα)^2
所以cosα=1/2;(cosα=-2舍去)
又(sinα)^4-(cosα)^4=(sina)^2-(cosα)^2=(3/2)cosα-(cosα)^2
所以(sinα)^4-(cosα)^4=(3/2)*(1/2)-(1/2)^2=1/2.
即(sinα)^4-(cosα)^4=1/2.