Complete the identity.
sec(x)sin(x)/tan(x) - 1 = 0
To complete the identity, we need to manipulate the given equation until it is in a form that is easily solvable.
Let's start by simplifying the equation:
sec(x)sin(x)/tan(x) - 1 = 0
sec(x)sin(x)/sin(x)/cos(x) - 1 = 0
sec(x)/cos(x) - 1 = 0
Next, let's replace sec(x)/cos(x) with its reciprocal, which is 1/cos(x):
1/cos(x) - 1 = 0
Now, we can simplify further by finding a common denominator:
1 - cos(x)/cos(x) = 0
Now, let's simplify the expression:
(1 - cos(x))/cos(x) = 0
Next, let's multiply both sides of the equation by cos(x) to eliminate the denominator:
1 - cos(x) = 0
Finally, let's reorganize the equation to isolate cos(x):
cos(x) = 1
So, the completed identity is cos(x) = 1.