Answer:
Proved See below
Step-by-step explanation:
Man this one is a world of its own :D Just a quick question are you a fellow Add Math student in O levels i remember this question from back in the day :D Anyhow Lets get started
For this question we need to know the following identities:
![1+tan^{2}x=sec^2x\\\\1+cot^2x=cosec^2x\\\\sin^2x+cos^2x=1](https://tex.z-dn.net/?f=1%2Btan%5E%7B2%7Dx%3Dsec%5E2x%5C%5C%5C%5C1%2Bcot%5E2x%3Dcosec%5E2x%5C%5C%5C%5Csin%5E2x%2Bcos%5E2x%3D1)
Lets solve the bottom most part first:
![1-\frac{1}{1-sec^2x} \\\\](https://tex.z-dn.net/?f=1-%5Cfrac%7B1%7D%7B1-sec%5E2x%7D%20%5C%5C%5C%5C)
Take LCM
![1-\frac{1}{1-sec^2x} \\\\\frac{1-sec^2x-1}{1-sec^2x} \\\\\frac{-sec^2x}{1-sec^2x} \\\\\frac{-(1+tan^2x)}{-tan^2x}](https://tex.z-dn.net/?f=1-%5Cfrac%7B1%7D%7B1-sec%5E2x%7D%20%5C%5C%5C%5C%5Cfrac%7B1-sec%5E2x-1%7D%7B1-sec%5E2x%7D%20%5C%5C%5C%5C%5Cfrac%7B-sec%5E2x%7D%7B1-sec%5E2x%7D%20%5C%5C%5C%5C%5Cfrac%7B-%281%2Btan%5E2x%29%7D%7B-tan%5E2x%7D)
now break the LCM
![\frac{-1}{-tan^2x}+\frac{-tan^2x}{-tan^2x}\\\\\frac{1}{tan^2x}+1\\\\cot^2x+1](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B-tan%5E2x%7D%2B%5Cfrac%7B-tan%5E2x%7D%7B-tan%5E2x%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7Btan%5E2x%7D%2B1%5C%5C%5C%5Ccot%5E2x%2B1)
because 1/tan = cot x
and furthermore,
![cot^2x+1\\cosec^2x](https://tex.z-dn.net/?f=cot%5E2x%2B1%5C%5Ccosec%5E2x)
now we solve the above part and replace the bottom most part that we solved with ![cosec^2x](https://tex.z-dn.net/?f=cosec%5E2x)
![\frac{1}{1-\frac{1}{cosec^2x} } \\\\\frac{1}{1-sin^2x} \\\\\frac{1}{cos^2x}\\\\sec^2x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1-%5Cfrac%7B1%7D%7Bcosec%5E2x%7D%20%7D%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B1-sin%5E2x%7D%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7Bcos%5E2x%7D%5C%5C%5C%5Csec%5E2x)
Hence proved! :D
7kg:4/9 bag
?kg:1 bag
7÷4/9 or 7×9/4=63/4 or 15.75. As a result, the unit rate is 15.75 kg of leaves per bag. Hope it help!
A.) 7^4x = 10
log base 10 (7^4X) = log base 10 (10)
4x log base 10 (7) = 1
4x (0.8451) = 1
3.3804x = 1
x = 0.2958
b.) ln(2) + ln(4x-1) = 5
ln (2 * 4x-1) = 5
ln (8x-2) = 5
log base (3) (8x-2) = 5
e^5 = 8x-2
e^5+2 = 8x
x = 18.8016
The greatest difference you can get is 42
The range of the integer is given as:
Smallest = -16
Largest = 26
So, the range is calculated as:
Range = Largest - Smallest
Substitute known values
Range = 26 - (-16)
Evaluate the difference
Range = 42
Hence, the greatest difference you can get is 42
Read more about range at:
https://brainly.in/question/6887467
77 green marbles
try googling the rest or 33/77=77%