Answer:
See explanation
Step-by-step explanation:
Simplify left and right parts separately.
<u>Left part:</u>
![\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}](https://tex.z-dn.net/?f=%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Ctan%5E2A%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Ccot%20%5E2A%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Csin%5E2A%7D%7B%5Ccos%5E2A%7D%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cleft%281%2B%5Cdfrac%7B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%5Cright%29%5Cleft%281%2B%5Cdfrac%7B%5Csin%5E2A%7D%7B%5Ccos%5E2A%7D%5Cright%29%5C%5C%20%5C%5C%3D%5Cdfrac%7B%5Csin%5E2A%2B%5Ccos%5E2A%7D%7B%5Csin%5E2A%7D%5Ccdot%20%5Cdfrac%7B%5Ccos%5E2A%2B%5Csin%5EA%7D%7B%5Ccos%5E2A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Ccos%5E2A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%5Ccos%5E2A%7D)
<u>Right part:</u>
![\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%5Csin%5E2A-%5Csin%5E4A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%281-%5Csin%5E2A%29%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2A%5Ccos%5E2A%7D)
Since simplified left and right parts are the same, then the equality is true.
Answer:
18
Step-by-step explanation:
Answer:
Some answers to the reducing fraction sheet
Q14 = 4/5 because divide 12 and 15 by 3
Q15=can't be reduced because 11 is a prime number so it can't be divided by anything
Q17=can't be reduced because 17 is a prime number
Q18=can't be reduced because 13 is a prime number
Q19=38/9 because 114 and 27 would be divided by 3
Q20= -1/1 because you would divide both 14,529 by itself would equal to - 1/1
I can only help you with this sheet I can't help you with the other one hope this was helpful! :)
X^4 + 2x^2 - 24
= (x^2 + 6)(x^2 - 4)
= (x^2 + 6)(x - 2)(x + 2)
x^4 - 9x^2 + 18
= (x^2 - 6)(x^2 - 3)
Answer: 80 minutes
Step-by-step explanation:
Hi, to answer this question we have to write an equation for each tank:
An empty 1200 gallon tank is filled with water at a rate of 6 gallons of water per minute.
So, the amount of water of the tank is equal to the filling rate, 6 liters per minute (6m)
- Tank 1 =0 (empty )+ 6m =6m
The second 1200 gallon tank full of water is being drained at a rate of 9 gallons per minute.
So, the amount of water in the tank is equal to the amount of water already in the tank (1200 g), minus the draining rate (9m)
Since both tanks will have the same amount of water:
6m = 1200-9m
Solving for m (minutes):
6m+9m= 1200
15m = 1200
m= 1200/15
m= 80 minutes
Feel free to ask for more if needed or if you did not understand something.