We will simplify the left hand side of the equation to look like the right
![\displaystyle \frac{1-sin(t)}{cos^{2}(t)} + \frac{1}{1 - sin(t)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B1-sin%28t%29%7D%7Bcos%5E%7B2%7D%28t%29%7D%20%20%2B%20%5Cfrac%7B1%7D%7B1%20-%20sin%28t%29%7D)
taking the LCM
![\displaystyle \frac{[1-sin(t)]^{2} + cos^{2}(t)}{[cos^{2}(t)][1 - sin(t)]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%5B1-sin%28t%29%5D%5E%7B2%7D%20%2B%20cos%5E%7B2%7D%28t%29%7D%7B%5Bcos%5E%7B2%7D%28t%29%5D%5B1%20-%20sin%28t%29%5D%7D)
expanding the binomial in the numerator
![\displaystyle \frac{[1 + sin^{2}(t) - 2sin(t) + cos^{2}(t)]}{[cos^{2}(t)][1 - sin(t)]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%5B1%20%2B%20sin%5E%7B2%7D%28t%29%20-%202sin%28t%29%20%2B%20cos%5E%7B2%7D%28t%29%5D%7D%7B%5Bcos%5E%7B2%7D%28t%29%5D%5B1%20-%20sin%28t%29%5D%7D)
Since sin²x + cos²x = 1
![\displaystyle \frac{[2 - 2sin(t)]}{[cos^{2}(t)][1 - sin(t)]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B%5B2%20-%202sin%28t%29%5D%7D%7B%5Bcos%5E%7B2%7D%28t%29%5D%5B1%20-%20sin%28t%29%5D%7D)
factoring out the 2 from the numerator
![\displaystyle \frac{2[1 - sin(t)]}{[cos^{2}(t)][1 - sin(t)]}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B2%5B1%20-%20sin%28t%29%5D%7D%7B%5Bcos%5E%7B2%7D%28t%29%5D%5B1%20-%20sin%28t%29%5D%7D)
1-sin(t) will cancel out
![\displaystyle \frac{2}{cos^{2}(t)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B2%7D%7Bcos%5E%7B2%7D%28t%29%7D)
since cos²(t) = 1/(sec²(t))
![2 sec^{2}(t)](https://tex.z-dn.net/?f=2%20sec%5E%7B2%7D%28t%29)
which is equal to the right hand side of our given equation.
So we verified the identity!
Answer:
The 24 wrestlers
Step-by-step explanation:
Divide 60 by 24. You get 5/2 16/6 15/6
Now divide 24 by 9. You get 8/3
Now make them have a common denominator: 5/2 * 3/3 = 15/6
8/3 * 2/2 = 16/6
The bigger fraction is 16/6, so its 24 wrestlers.
I hope this helped, please mark Brainliest, thank you!
Answer:
ad, 12 and 3
Step-by-step explanation: