Answer:
See explanation
Step-by-step explanation:
Prove equality
![(1-\cot A)^2+(\tan A-1)^2=4\csc 2A(\csc 2A-1)](https://tex.z-dn.net/?f=%281-%5Ccot%20A%29%5E2%2B%28%5Ctan%20A-1%29%5E2%3D4%5Ccsc%202A%28%5Ccsc%202A-1%29)
Consider left and right parts separately.
<u>Left part:</u>
![(1-\cot A)^2+(\tan A-1)^2\\ \\=1-2\cot A+\cot^2 A+\tan^2 A-2\tan A+1\\ \\=(1+\cot^2 A)+(1+\tan^2 A)-2(\cot A+\tan A)\\ \\=\dfrac{1}{\sin^2 A}+\dfrac{1}{\cos ^2A}-2\dfrac{\cos^2 A+\sin^2 A}{\cos A\sin A}\\ \\=\dfrac{1}{\sin^2 A}+\dfrac{1}{\cos ^2A}-\dfrac{2}{\cos A\sin A}\\ \\=\dfrac{\cos^2A+\sin^2A-2\cos A\sin A}{\cos ^2A\sin ^2A}\\ \\=\dfrac{1-\sin 2A}{\frac{1}{4}\cdot 4\cdot \cos^2A\sin^2 A}\\ \\=\dfrac{1-\sin 2A}{\frac{1}{4}\cdot \sin^22 A}\\ \\=4\dfrac{1-\sin 2A}{\sin^22 A}](https://tex.z-dn.net/?f=%281-%5Ccot%20A%29%5E2%2B%28%5Ctan%20A-1%29%5E2%5C%5C%20%5C%5C%3D1-2%5Ccot%20A%2B%5Ccot%5E2%20A%2B%5Ctan%5E2%20A-2%5Ctan%20A%2B1%5C%5C%20%5C%5C%3D%281%2B%5Ccot%5E2%20A%29%2B%281%2B%5Ctan%5E2%20A%29-2%28%5Ccot%20A%2B%5Ctan%20A%29%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2%20A%7D%2B%5Cdfrac%7B1%7D%7B%5Ccos%20%5E2A%7D-2%5Cdfrac%7B%5Ccos%5E2%20A%2B%5Csin%5E2%20A%7D%7B%5Ccos%20A%5Csin%20A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1%7D%7B%5Csin%5E2%20A%7D%2B%5Cdfrac%7B1%7D%7B%5Ccos%20%5E2A%7D-%5Cdfrac%7B2%7D%7B%5Ccos%20A%5Csin%20A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B%5Ccos%5E2A%2B%5Csin%5E2A-2%5Ccos%20A%5Csin%20A%7D%7B%5Ccos%20%5E2A%5Csin%20%5E2A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1-%5Csin%202A%7D%7B%5Cfrac%7B1%7D%7B4%7D%5Ccdot%204%5Ccdot%20%5Ccos%5E2A%5Csin%5E2%20A%7D%5C%5C%20%5C%5C%3D%5Cdfrac%7B1-%5Csin%202A%7D%7B%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20%5Csin%5E22%20A%7D%5C%5C%20%5C%5C%3D4%5Cdfrac%7B1-%5Csin%202A%7D%7B%5Csin%5E22%20A%7D)
<u>Right part:</u>
![\csc 2A=\dfrac{1}{\sin 2A}](https://tex.z-dn.net/?f=%5Ccsc%202A%3D%5Cdfrac%7B1%7D%7B%5Csin%202A%7D)
Hence
![4\csc 2A(\csc 2A-1)\\ \\=4\cdot \dfrac{1}{\sin 2A}\cdot \left(\dfrac{1}{\sin 2A}-1\right)\\ \\=4\cdot \dfrac{1}{\sin 2A}\cdot \dfrac{1-\sin 2A}{\sin 2A}\\ \\=4\dfrac{1-\sin 2A}{\sin^2 2A}](https://tex.z-dn.net/?f=4%5Ccsc%202A%28%5Ccsc%202A-1%29%5C%5C%20%5C%5C%3D4%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Csin%202A%7D%5Ccdot%20%5Cleft%28%5Cdfrac%7B1%7D%7B%5Csin%202A%7D-1%5Cright%29%5C%5C%20%5C%5C%3D4%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Csin%202A%7D%5Ccdot%20%5Cdfrac%7B1-%5Csin%202A%7D%7B%5Csin%202A%7D%5C%5C%20%5C%5C%3D4%5Cdfrac%7B1-%5Csin%202A%7D%7B%5Csin%5E2%202A%7D)
Since left and right parts are the same, the equality is true.
Answer: 25??
Step-by-step explanation: $8×25= $200
i dont know if thats your answer thats just all the adults that could get in for $200.
-Zoey Lee
<h2 />
Check the picture below.
the shortest path from a point to a line, is simply the perpendicular path to it.
-5 = a/18
multiply by 18 on each side
-5 * 18 = a/18 * 18
-90 = a
Answer: a = -90
Step-by-step explanation:
easy to look up : mili stands for 1/1000
so,
500 ml are 500/1000 liters.
25 ml are 25/1000 liters (a tiny glass).
and 1 Iiter is of course, 1000/1000 liters (1000 ml).
4 liters 500 ml are then
4×1000/1000 + 500/1000 = 4500/1000 l = 4500 ml.
how many glasses of 25 ml can be filled with that ?
this is the same question as into how many parts of 25 can 4500 be split ? or, how often does 25 fit into 4500 ?
all this is done by division :
4500 / 25 = 180
so, 180 of such glasses can be filled.