已知sin(a+b)=0.5,sin(a-b)=1/3,则【tan(a+b)—tana——tanb】/【(tanb)tanbtan(a+b)】=?
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已知sin(a+b)=0.5,sin(a-b)=1/3,则【tan(a+b)—tana——tanb】/【(tanb)tanbtan(a+b)】=?
sina cosb + cosa sinb = 1/2
sina cosb - cosa sinb = 1/3
相加:
2 sina cosb = 5/6
sina cosb = 5/12
相减:
2 cosa sinb = 1/6
cosa sinb = 1/12
则:
sina cosb /(cosa sinb)=5
sina /cosa = 5 sinb / cosb
所以tan a = 5 tan b
tan(a+b)=[tan a + tan b]/[1- tan a tan b]
= (5tanb+tanb)/(1-5tanb tanb)
=6tanb /(1-5tanbtanb)
[tan(a+b)-tana-tanb]/[tanb tanb tan(a+b)]
= [6tanb/(1-5tanbtanb) - 5tanb - tanb]/[tanb tanb 6 tanb/(1-5tanbtanb)]
分子分母乘以(1-5tanbtanb)
= [6tanb - 6tanb(1-5tanbtanb)]/[6tanbtanbtanb]
= [30tanbtanbtanb]/[6tanbtanbtanb]
=5
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