How do you simplify #csc θsec θ - cot θ#?
Lets start by using some trig identities to put the original statement into terms of
At this point it would be helpful to have a common denominator. We can do that by multiplying the top and bottom of the second term by
Now we can combine the numerators over
We can use the Pythagorean theorem to simplify the numerator. The Pythagorean theorem states that;
Rearranging the terms we get;
Now we can make the substitution for the numerator.
Which is the definition of