ANSWER
See explanation.
EXPLANATION
We want to very the identity:
![1 - 2 \cos^{2} (x) = 2 \sin^{2} (x) - 1](https://tex.z-dn.net/?f=1%20-%202%20%5Ccos%5E%7B2%7D%20%28x%29%20%3D%202%20%5Csin%5E%7B2%7D%20%28x%29%20-%201)
Let us take the Left hand side and work it out to get the right hand side.
![1 - 2 \cos^{2} (x)](https://tex.z-dn.net/?f=1%20-%202%20%5Ccos%5E%7B2%7D%20%28x%29)
Recall the Pythagorean Identity:
![\cos^{2} (x) + \sin^{2} (x) = 1](https://tex.z-dn.net/?f=%20%5Ccos%5E%7B2%7D%20%28x%29%20%2B%20%20%5Csin%5E%7B2%7D%20%28x%29%20%3D%201)
Make cos²(x) the subject.
![\cos^{2} (x) = 1 - \sin^{2} (x)](https://tex.z-dn.net/?f=%20%5Ccos%5E%7B2%7D%20%28x%29%20%3D%201%20-%20%20%5Csin%5E%7B2%7D%20%28x%29)
We substitute this into our expression to get:
![1 - 2 (1 - \sin^{2} (x) )](https://tex.z-dn.net/?f=1%20-%202%20%281%20-%20%20%5Csin%5E%7B2%7D%20%28x%29%20%29)
Expand:
![1 - 2 + 2\sin^{2} (x)](https://tex.z-dn.net/?f=1%20-%202%20%2B%202%5Csin%5E%7B2%7D%20%28x%29%20)
Simplify
![- 1+ 2\sin^{2} (x)](https://tex.z-dn.net/?f=%20-%201%2B%202%5Csin%5E%7B2%7D%20%28x%29%20)
We can rewrite to get;
![2\sin^{2} (x) - 1](https://tex.z-dn.net/?f=2%5Csin%5E%7B2%7D%20%28x%29%20%20-%201)
Therefore:
![1 - 2 \cos^{2} (x) = 2 \sin^{2} (x) - 1](https://tex.z-dn.net/?f=1%20-%202%20%5Ccos%5E%7B2%7D%20%28x%29%20%3D%202%20%5Csin%5E%7B2%7D%20%28x%29%20-%201)
Answer:
The P-value is less than 0.005
Step-by-step explanation:
took the test good luck!
Because k is constant, we can find it by multiplying the x-coordinate by the y-coordinate. If y varies inversely as x and x = 5 when y = 2, the constant of variation is k = xy = 5(2) = 10.
8
, 12 and 18 are less than 19 and have more factors than 19
, 21
, 23 and 25
.
Answer:
No, sadly ;-;
Step-by-step explanation: