The goal to proving identities is to transform one side into the other. We can only pick one side to transform while the other side stays the same the entire time. The general rule of thumb is to transform the more complicated side (though there may be exceptions to this guideline).
So I'll take the left hand side and try to turn it into ![\csc^2( B )](https://tex.z-dn.net/?f=%5Ccsc%5E2%28%20B%20%29)
One way we can do that is through the following steps:
![\frac{\tan(B) + \cot(B)}{\tan(B)} = \csc^2(B)\\\\\frac{\tan(B)}{\tan(B)} + \frac{\cot(B)}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\frac{1}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\cot(B) = \csc^2(B)\\\\1 + \cot^2(B) = \csc^2(B)\\\\1 + \frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)}{\sin^2(B)}+\frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)+cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{1}{\sin^2(B)} = \csc^2(B)\\\\\csc^2(B)=\csc^2(B) \ \ {\Large \checkmark}\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctan%28B%29%20%2B%20%5Ccot%28B%29%7D%7B%5Ctan%28B%29%7D%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C%5Cfrac%7B%5Ctan%28B%29%7D%7B%5Ctan%28B%29%7D%20%2B%20%5Cfrac%7B%5Ccot%28B%29%7D%7B%5Ctan%28B%29%7D%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C1%20%2B%20%5Ccot%28B%29%2A%5Cfrac%7B1%7D%7B%5Ctan%28B%29%7D%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C1%20%2B%20%5Ccot%28B%29%2A%5Ccot%28B%29%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C1%20%2B%20%5Ccot%5E2%28B%29%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C1%20%2B%20%5Cfrac%7Bcos%5E2%28B%29%7D%7B%5Csin%5E2%28B%29%7D%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C%5Cfrac%7Bsin%5E2%28B%29%7D%7B%5Csin%5E2%28B%29%7D%2B%5Cfrac%7Bcos%5E2%28B%29%7D%7B%5Csin%5E2%28B%29%7D%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C%5Cfrac%7Bsin%5E2%28B%29%2Bcos%5E2%28B%29%7D%7B%5Csin%5E2%28B%29%7D%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C%5Cfrac%7B1%7D%7B%5Csin%5E2%28B%29%7D%20%3D%20%5Ccsc%5E2%28B%29%5C%5C%5C%5C%5Ccsc%5E2%28B%29%3D%5Ccsc%5E2%28B%29%20%5C%20%5C%20%7B%5CLarge%20%5Ccheckmark%7D%5C%5C%5C%5C)
Since we've shown that the left hand side transforms into the right hand side, this verifies the equation is an identity.
Answer:
5) 30.0m
6) 34.0mi
7) 11.0ft
8) 17.0 km
(all rounded off to the nearest tenth)
Step-by-step explanation:
Please see attached pictures for the full solution.
9 miles he traveled on tuesday, why? because if you were to draw a line connecting the dots and went to the x coordinate 60 (hour in minutes) on the line you drew, you can see its also at 9 miles on the y coordinate
Hope Your Thanksgiving Goes Well, Here's A Turkey
-TheKoolKid1O1