tan^2a=2tan^2b+1则cos2a+sin^2b等于多少要过程

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tan^2a=2tan^2b+1则cos2a+sin^2b等于多少要过程tan^2a=2tan^2b+1则cos2a+sin^2b等于多少要过程tan^2a=2tan^2b+1则cos2a+sin^2

tan^2a=2tan^2b+1则cos2a+sin^2b等于多少要过程
tan^2a=2tan^2b+1则cos2a+sin^2b等于多少
要过程

tan^2a=2tan^2b+1则cos2a+sin^2b等于多少要过程
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.