Question

tan^2a=2tan^2b+1则cos2a+sin^2b等于多少

Answer 1

答案是0,

(tana)^2=2(tanb)^2+1;

(sina/cosa)^2=2(sinb/cosb)^2+1;

[(sina)^2]*[(cosb)^2]

=2[(sinb)^2]*[(cosa)^2]+[(cosa)^2][(cosb)^2];

[1-(cosa)^2][1-(sinb)^2]

=2[(sinb)^2]*[(cosa)^2]+[(cosa)^2]*[1-(sinb)^2];

化简得:(sinb)^2+2(cosa)^2=1;

由于 (cosa)^2=(1-cos2a)/2;

所以 sin^2b+cos2a+1=1；

所以 cos2a+sin^2b=0.