Question

已知α为锐角,且sinα=7/8sinβ,tanα=1/4tanβ,求α

Answer 1

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