Question

已知sina+2cosa=0求3sina2+sinacosa-2cosa2

Answer 1

sina+2cosa=0,sina=-2cosa,
sina/cosa=tana=-2
即tana=-2
3sin²a+sinacosa-2cos²a
=[3sin²a+sinacosa-2cos²a]/(sin²a+cos²a)
=[3tan²a+tana-2]/(tan²a+1)
=(12-2-2)/(4+1)
=8/5

Answer 2

sina+2cosa=0
tana=-2
3sin^2a+sinacosa-2cos^2a
=(3sin^2a+sinacosa-2cos^2a)/(sin^2a+cos^2a)
=(3tan^2a+tana-2)/(tan^2a+1)
=(3*4-2-2)/(4+1)
=8/5

追问

为什么tana=-2

追答

sina+2cosa=0

sina=-2cosa
tana=sina/cosa=-2

Answer 3

sina+2cosa=0 tana=-2
3sina2+sinacosa-2cosa2=（3sin²a+sinacosa-2cos²a）
=（3sin²a+sinacosa-2cos²a)/(sin²a+cos²a)
=（3tan²a+tana-2)/(tan²a+1)
=(3x(-2)²+(-2)-2)/((-2)²+1)
=（12-2-2)/(4+1)
=8/5

Answer 4

sina+2cosa=0
sina = -2cosa

3sina2+sinacosa-2cosa2
= 3(-2cosa)^2 + (-2cosa)cosa - 2(cosa)^2
= 12(cosa)^2 - 2(cosa)^2 - 2(cosa)^2
= 8(cosa)^2