Question

已知sin(a+b)=1/2，sin(a－b)=1/3，求tanacotb的值

Answer 1

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

sin(a－b)=1/3
sinacosb-cosasinb=1/3

两式相减得
2sinacosb=5/6................(1)

两式相减得
2cosasinb=1/6................(2)

(1)÷(2)得
tanacotb=5

Answer 2

解: tanacotb
=sina/cosa×cosb/sinb
=sinacosb/(cosasinb)
sin(a+b)=1/2，
sinacosb+cosasinb=1/2......(1)
sin(a－b)=1/3
sinacosb-cosasinb=1/3.......(2)
(1)+(2)得 2sinacosb=5/6 sinacosb=5/12
(1)-(2)得 2cosasinb=1/6 cosasinb=1/12
则 tanacotb
=sinacosb/(cosasinb)
=5/12÷1/12
=5
祝你开心