已知α为锐角,且sinα=7/8sinβ,tanα=1/4tanβ,求α

已知α为锐角,且sinα=7/8sinβ,tanα=1/4tanβ,求α
已知α为锐角,且sinα=7/8sinβ,tanα=1/4tanβ,求α

已知α为锐角,且sinα=7/8sinβ,tanα=1/4tanβ,求α
sina=7/8sinb
tana=1/4tanb
sina/cosa=1/4sinb/cosb
cosa=7/2cosb
sin^2a+co^2a=(7/8sinb)^2+(7/2cosb)^2=1
49/64(sinb)^2+49/4(cosb)^2=1
49/64+(15*49)/64(cosb)^2=1
(cosb)^2=1/49
cosb=1/7
cosa=1/2
a=60