已知tana=3,则2sin^2a+4sinacosa-9cos^2a的值为

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已知tana=3,则2sin^2a+4sinacosa-9cos^2a的值为
已知tana=3,则2sin^2a+4sinacosa-9cos^2a的值为

已知tana=3,则2sin^2a+4sinacosa-9cos^2a的值为
2sin^2a+4sinacosa-9cos^2a
=(2sin^2a+4sinacosa-9cos^2a)/(sin^2a+cos^2a)
=(2tan^2a+4tana-9)/(tan^2a+1)*上下同时除于cos^2a*
知tana=3
所以原式=(2*9+4*3-9)/(9+1)
=2.1

{4sinacosa+4sinacosa-9(cosa^2-sina^2)}\(sina^2+cosa^2)=(9sina^2+8sinacosa-9cosa^2)\(sina^2+cosa^2)=(9tana^2+8tana-9)\(tana^2+1)
=(81+24-9)\(9+1)=9.6

2sin^2a+4sinacosa-9cos^2a
=2-11cos^2a+4cos^2a*tana
tana=3,cos^2a=1/(1+tan^2a)=1/10
代入,得原式=2-11/10+4*3/10=19/10