Question

if sin(a+b)/sin(a-b)= 7/3 then tan a /tan b​

Answer 1

Step-by-step explanation:

Sin(a+b)/sin(a-b) =7/3 {given}-----------(equ1)

Now,

since, sin(a+b)=sinacosb+cosasinb-----(equ2)

And, sin(a-b) =sinacosb-cosasinb-------(equ3)

put the value of equ2 and equ3 In equ1

=sinacosb+cosasinb/sinacosb-cosasinb=7/3

=3sinacosb+3cosasinb=7sinacosb-7cosasinb

=3cosasinb+7cosasinb=7sinacosb-3sinacosb

=10cosasinb=4sinacosb

=10/4=sinacosb/cosasinb

=10/4=sina/cosa/sinb/cosb

Therefore, tana/tanb=10/4

i hope it's clear to you☺