Sure, let's verify the following mathematical statement step by step:
1/sin(x) - 1/cos(x) = (cos(x) - sin(x)) / (sin(x)cos(x))
Step 1:
First, find common denominators on the left side of the equation which are sin(x) and cos(x).
To do that we need to multiply the first term by cos(x)/cos(x) and the second term by sin(x)/sin(x):
(cos(x)/sin(x)cos(x)) - (sin(x)/sin(x)cos(x))
Step 2:
Now you can combine the two fractions as they have the same denominator:
(cos(x) - sin(x)) / (sin(x)cos(x))
So, the given mathematical statement is true:
1/sin(x) - 1/cos(x) = (cos(x) - sin(x)) / (sin(x)cos(x))
and we have our proof done!