Answer:
(f+g)(x) = -5x-3
(f+g)(-4)= 17
Step-by-step explanation:
you add f(x) to g(x) for the first part.
the second part you add them but plug in -4 for x.
Answer:
First, we know that:
cot(x) = cos(x)/sin(x)
csc(x) = 1/sin(x)
I can't know for sure what is the exact equation, so I will assume two cases.
The first case is if the equation is:
![\frac{cot(x)}{sin(x)} - csc(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%28x%29%7D%7Bsin%28x%29%7D%20-%20csc%28x%29)
if we replace cot(x) and csc(x) we get:
![\frac{cot(x)}{sin(x)} - csc(x) = \frac{cos(x)}{sin(x)} \frac{1}{sin(x)} - \frac{1}{sin(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%28x%29%7D%7Bsin%28x%29%7D%20-%20csc%28x%29%20%3D%20%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%20%5Cfrac%7B1%7D%7Bsin%28x%29%7D%20%20-%20%5Cfrac%7B1%7D%7Bsin%28x%29%7D)
Now let's we can rewrite this as:
![\frac{cos(x)}{sin(x)} \frac{1}{sin(x)} - \frac{1}{sin(x)} =\frac{cos(x)}{sin^2(x)} - \frac{1}{sin(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%20%5Cfrac%7B1%7D%7Bsin%28x%29%7D%20%20-%20%5Cfrac%7B1%7D%7Bsin%28x%29%7D%20%3D%5Cfrac%7Bcos%28x%29%7D%7Bsin%5E2%28x%29%7D%20-%20%5Cfrac%7B1%7D%7Bsin%28x%29%7D)
![\frac{cos(x)}{sin^2(x)} - \frac{sin(x)}{sin^2(x)} = \frac{cos(x) - sin(x)}{sin^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29%7D%7Bsin%5E2%28x%29%7D%20%20-%20%5Cfrac%7Bsin%28x%29%7D%7Bsin%5E2%28x%29%7D%20%3D%20%5Cfrac%7Bcos%28x%29%20-%20sin%28x%29%7D%7Bsin%5E2%28x%29%7D)
We can't simplify it more.
Second case:
If the initial equation was
![\frac{cot(x)}{sin(x) - csc(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bcot%28x%29%7D%7Bsin%28x%29%20-%20csc%28x%29%7D)
Then if we replace cot(x) and csc(x)
![\frac{cos(x)}{sin(x)}*\frac{1}{sin(x) - 1/sin(x)} = \frac{cos(x)}{sin(x)}*\frac{1}{sin^2(x)/sin(x) - 1/sin(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%2A%5Cfrac%7B1%7D%7Bsin%28x%29%20-%201%2Fsin%28x%29%7D%20%3D%20%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%2A%5Cfrac%7B1%7D%7Bsin%5E2%28x%29%2Fsin%28x%29%20-%201%2Fsin%28x%29%7D)
This is equal to:
![\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%2A%5Cfrac%7Bsin%28x%29%7D%7Bsin%5E2%28x%29%20-%201%7D)
And we know that:
sin^2(x) + cos^2(x) = 1
Then:
sin^2(x) - 1 = -cos^2(x)
So we can replace that in our equation:
![\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1} = \frac{cos(x)}{sin(x)}*\frac{sin(x)}{-cos^2(x)} = -\frac{cos(x)}{cos^2(x)}*\frac{sin(x)}{sin(x)} = - \frac{1}{cos(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%2A%5Cfrac%7Bsin%28x%29%7D%7Bsin%5E2%28x%29%20-%201%7D%20%3D%20%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%2A%5Cfrac%7Bsin%28x%29%7D%7B-cos%5E2%28x%29%7D%20%3D%20-%5Cfrac%7Bcos%28x%29%7D%7Bcos%5E2%28x%29%7D%2A%5Cfrac%7Bsin%28x%29%7D%7Bsin%28x%29%7D%20%20%3D%20-%20%5Cfrac%7B1%7D%7Bcos%28x%29%7D)
Answer:
42
Step-by-step explanation:
16 dividied by 4 is 4
4 minus 4 is 0
and 0 plus 42 is 42
Answer:
January
Step-by-step explanation:
A counterexample is something that proves the statement false.
January is a month that starts with J that is not a summer month.
That proves the statement false
4+21-18
25-18
7 is the correct answer