Answer:
the rate compounded semi-annually is compounded twice in a year. thus, this rate is higher than the rate compounded annually which is compounded once in a year
Step-by-step explanation:
The formula for calculating future value:
FV = P (1 + r/m)^mn
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
For example, there are two banks
Bank A offers 10% rate with semi-annual compounding
Bank B offers 10% rate with annual compounding.
If you deposit $100, the amount you would have after 2 years in each bank is
A = 100x (1 + 0.1/2)^4 = 121.55
B = 100 x (1 + 0.1)^2 = 121
The interest in bank a is 0.55 higher than that in bank B
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
Hope this helps!! If u want me to answer any more questions just ask! Have a nice day!
Answer:
do u even still need the answer its been aweek since you asked it and it was due that same day
Step-by-step explanation:
Answer:
7 9/10
Step-by-step explanation:
cuz mah brain big
