1)
here, we do the left-hand-side
![\bf [sin(x)+cos(x)]^2+[sin(x)-cos(x)]^2=2 \\\\\\\ [sin^2(x)+2sin(x)cos(x)+cos^2(x)]\\\\+~ [sin^2(x)-2sin(x)cos(x)+cos^2(x)] \\\\\\ 2sin^2(x)+2cos^2(x)\implies 2[sin^2(x)+cos^2(x)]\implies 2[1]\implies 2](https://tex.z-dn.net/?f=%5Cbf%20%5Bsin%28x%29%2Bcos%28x%29%5D%5E2%2B%5Bsin%28x%29-cos%28x%29%5D%5E2%3D2%0A%5C%5C%5C%5C%5C%5C%5C%0A%5Bsin%5E2%28x%29%2B2sin%28x%29cos%28x%29%2Bcos%5E2%28x%29%5D%5C%5C%5C%5C%2B~%20%5Bsin%5E2%28x%29-2sin%28x%29cos%28x%29%2Bcos%5E2%28x%29%5D%0A%5C%5C%5C%5C%5C%5C%0A2sin%5E2%28x%29%2B2cos%5E2%28x%29%5Cimplies%202%5Bsin%5E2%28x%29%2Bcos%5E2%28x%29%5D%5Cimplies%202%5B1%5D%5Cimplies%202)
2)
here we also do the left-hand-side
![\bf \cfrac{2-cos^2(x)}{sin(x)}=csc(x)+sin(x) \\\\\\ \cfrac{2-[1-sin^2(x)]}{sin(x)}\implies \cfrac{2-1+sin^2(x)}{sin(x)}\implies \cfrac{1+sin^2(x)}{sin(x)} \\\\\\ \cfrac{1}{sin(x)}+\cfrac{sin^2(x)}{sin(x)}\implies csc(x)+sin(x)](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B2-cos%5E2%28x%29%7D%7Bsin%28x%29%7D%3Dcsc%28x%29%2Bsin%28x%29%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B2-%5B1-sin%5E2%28x%29%5D%7D%7Bsin%28x%29%7D%5Cimplies%20%5Ccfrac%7B2-1%2Bsin%5E2%28x%29%7D%7Bsin%28x%29%7D%5Cimplies%20%5Ccfrac%7B1%2Bsin%5E2%28x%29%7D%7Bsin%28x%29%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B1%7D%7Bsin%28x%29%7D%2B%5Ccfrac%7Bsin%5E2%28x%29%7D%7Bsin%28x%29%7D%5Cimplies%20csc%28x%29%2Bsin%28x%29)
3)
here, we do the right-hand-side
<span>√63 = 3√7 is your answer</span>
Assume that the radius of the circle is 1.
The diagonal of the square is 2. By the Pythagorean Theorem, the side of the square of a right triangle will be 2/sqrt(2).
Finally, the ratio of the square to the circle, in area, will be
(2/sqrt(2))^2 : pi*(1)^2 = 2 : pi
We can conclude that the white area is about 35%.
1. Identify valid x and y points by doing vertical and horizontal line test
2. Use these toolkit to find the appropriate function
Answer: A
Step-by-step explanation:
For this problem, we need to understand how translations work.
As you can see, the triangles only slide to the right side, along the x axis. Therefore, we can eliminate B and C.
Now, we can see that the triangle has shifted by +8 units. Therefore, A is the correct answer.
