已知α为锐角,且sinα=7/8sinβ,tanα=1/4tanβ,求α
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![已知α为锐角,且sinα=7/8sinβ,tanα=1/4tanβ,求α](/uploads/image/z/8771892-60-2.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%E4%B8%BA%E9%94%90%E8%A7%92%2C%E4%B8%94sin%CE%B1%3D7%2F8sin%CE%B2%2Ctan%CE%B1%3D1%2F4tan%CE%B2%2C%E6%B1%82%CE%B1)
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