若asecα-2tanα=1,bsecα+tanα=2则a^2+b^2=

若asecα-2tanα=1,bsecα+tanα=2则a^2+b^2=
若asecα-2tanα=1,bsecα+tanα=2则a^2+b^2=

若asecα-2tanα=1,bsecα+tanα=2则a^2+b^2=
a*secα=1+2tanα
a=cosα+2sinα
b*secα=2-tanα
b=2cosα-sinα
a^2+b^2=(cosα)^2+4cosα*sinα+4(sinα)^2+4(cosα)^2-4cosα*sinα+(sinα)^2=
=[(cosα)^2+(sinα)^2]+4[(sinα)^2+(cosα)^2]+4[cosα*sinα-cosα*sinα]=
=1+4=5