Question

求解 已知 sin(a+b)=1/2 ,sin(a_b)=1/3,求证:tan a=5tan b

求解:已知 sin(a+b)=1/2 ,sin(a_b)=1/3,求证:tan a=5tan b

Answer 1

sin(a+b)=sinacosb+cosasinb=1/2
sin(a-b)=sinacosb-cosasinb=1/3
所以sinacosb=(1/2+1/3)/2=5/12
cosasinb=(1/2-1/3)/2=1/12
相除
sinacosb/cosasinb=5
(sina/cosa)/(sinb/cosb)=5
tana/tanb=5
所以tana=5tanb

Answer 2

sinacosb+sinbcosa=1/2
sinacosb-sinbcosa=1/3
2sinacosb=5/6
2sinbcosa=1/6
tana/tanb=5
tana=5tanb

Answer 3

sin(a+b) = sinacosb + cosasinb = 1/2
sin(a-b) = sinacosb - cosasinb = 1/3

所以 6（sinacosb+cosasinb） = 1.5*6*(sinacosb -cosasinb)

所以 15cosasinb ＝ 3sinacosb

sinacosb/(cosasinb) = 5

tana/tanb = 5

tana = 5tanb