已知sina+cosa=0,求sin^2a+2sinacosa+cos^2a

问题描述:

已知sina+cosa=0,求sin^2a+2sinacosa+cos^2a

sin^2a表示(sina)²吧
∵sina+cosa=0
∴tana=-1
∵sin^2a+cos^2a=1
∴sin^2a+2sinacosa+cos^2a=(sin^2a+2sinacosa+cos^2a)/(sin^2a+cos^2a)
在分子分母同除以cos^2a
即(sin^2a+2sinacosa+cos^2a)/(sin^2a+cos^2a)
=(tan^2a+2tana+1)/(tan^2a+1) 代入tana=-1
=0.啊,对不起对不起是已知3sina+cosa=o抱歉抱歉没关系只是可以算得tana=-1/3其他都一样即(sin^2a+2sinacosa+cos^2a)/(sin^2a+cos^2a)=(tan^2a+2tana+1)/(tan^2a+1) 代入tana=-1/3=2/5.