Simplify: cos x cos x
----- + -----
sec x-1 sec x+1
is that
cosx/(secx - 1) + cosx/(secx + 1) ???
of so, then using a common denominator , ...
(cosx(secx + 1) + cosx(secx - 1)) / (sec^2 x - 1)
= cosx(2secx)/tan^2x
= cosx(2/cosx) ( cos^2x/sin^2x
= 2cot^2 x
To simplify the given expression, we need to find a common denominator for the two fractions and combine them.
First, let's simplify the denominators:
1. Simplify sec(x) - 1:
We know that sec(x) is the reciprocal of cos(x). So, sec(x) - 1 can be rewritten as (1/cos(x)) - 1.
To find a common denominator, we multiply the first fraction by (cos(x)/cos(x)):
(1/cos(x)) - 1 = (1/cos(x)) * (cos(x)/cos(x)) - 1 = (cos(x) - 1)/cos(x).
2. Simplify sec(x) + 1:
Similarly, sec(x) + 1 can be rewritten as (1/cos(x)) + 1.
To find a common denominator, we multiply the first fraction by (cos(x)/cos(x)):
(1/cos(x)) + 1 = (1/cos(x)) * (cos(x)/cos(x)) + 1 = (cos(x) + 1)/cos(x).
Now, we can rewrite the expression with the simplified denominators:
cos(x)/((cos(x) - 1)*(cos(x) + 1)).
And since the denominators share the same terms but with different signs, we can combine them into a single fraction:
cos(x)/(cos^2(x) - 1).
The simplified expression is: cos(x)/(cos^2(x) - 1).
Please note that there might be other possible simplifications depending on the context and the specific instructions given.