Answer:
The proof is given below.
Step-by-step explanation:
Given: ( the correct question and ans is as follow )
sin (x + y) = 3sin ( x - y)
To Prove
tan x = 2 tan y
Proof:

Using the identities

we get

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

The missing numerator that will make the rational expressions equivalent is (82x + 7) / (12x + 42)
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the missing numerator, hence:
82x + 7 = y * 6(2x+7)
82x + 7 = y * (12x + 42)
y = (82x + 7) / (12x + 42)
Find out more on equation at: brainly.com/question/2972832