An identity is true for all values of x, the more appropriate word here would be equation.
We have to find the value of x for which the equation 7*sin x = 6*cos x.
7*sin x = 6*cos x
=> sin x / cos x = 6/7
=> tan x = 6/7
=> x = arc tan(6/7)
=> x = 40.60 degrees
The value of x that makes 7sin x = 6cos x is 40.60 degrees
This is an homogenous equation. For solving the equation, we'll have to create the tangent function.
Knowing that tan x = sin x/cos x, we'll create tangent function by dividing all equation by cos x:
7sin x/cos x - 6 = 0
7tan x - 6 = 0
We'll add 6 both sides:
7tan x = 6
We'll divide by 7:
tan x = 6/7
We've get an elementary equation:
x = arctan (6/7) + k*pi