6 x minus 4 and start fraction 9 over 10
Answer: You meant a picture?
Step-by-step explanation: The model is here:
Answer:
1
Step-by-step explanation:
First, convert all the secants and cosecants to cosine and sine, respectively. Recall that
and
.
Thus:
![\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bsec%28x%29%7D%7Bcos%28x%29%7D%20-%5Cfrac%7Bsin%28x%29%7D%7Bcsc%28x%29cos%5E2%28x%29%7D)
![=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20%7D%7Bcos%28x%29%7D%20-%5Cfrac%7Bsin%28x%29%7D%7B%5Cfrac%7B1%7D%7Bsin%28x%29%7Dcos%5E2%28x%29%20%7D)
Let's do the first part first: (Recall how to divide fractions)
![\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20%7D%7Bcos%28x%29%7D%3D%5Cfrac%7B1%7D%7Bcos%28x%29%7D%20%5Ccdot%20%5Cfrac%7B1%7D%7Bcos%28x%29%7D%3D%5Cfrac%7B1%7D%7Bcos%5E2%28x%29%7D)
For the second term:
![\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28x%29%7D%7B%5Cfrac%7Bcos%5E2%28x%29%7D%7Bsin%28x%29%7D%20%7D%20%3D%5Cfrac%7Bsin%28x%29%7D%7B1%7D%20%5Ccdot%5Cfrac%7Bsin%28x%29%7D%7Bcos%5E2%28x%29%7D%3D%5Cfrac%7Bsin%5E2%28x%29%7D%7Bcos%5E2%28x%29%7D)
So, all together: (same denominator; combine terms)
![\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bcos%5E2%28x%29%7D-%5Cfrac%7Bsin%5E2%28x%29%7D%7Bcos%5E2%28x%29%7D%3D%5Cfrac%7B1-sin%5E2%28x%29%7D%7Bcos%5E2%28x%29%7D)
Note the numerator; it can be derived from the Pythagorean Identity:
![sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)](https://tex.z-dn.net/?f=sin%5E2%28x%29%2Bcos%5E2%28x%29%3D1%3B%20cos%5E2%28x%29%3D1-sin%5E2%28x%29)
Thus, we can substitute the numerator:
![\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1](https://tex.z-dn.net/?f=%5Cfrac%7B1-sin%5E2%28x%29%7D%7Bcos%5E2%28x%29%7D%3D%5Cfrac%7Bcos%5E2%28x%29%7D%7Bcos%5E2%28x%29%7D%3D1)
Everything simplifies to 1.
Answer:
Step-by-step explanation:
subtract llol
first 1
x . y
1 . 2
3 . 4 rewrite =y/x
2-4/1-3
-2/2=-1
do for the rest bye