<span> I am assuming you want to prove:
csc(x)/[1 - cos(x)] = [1 + cos(x)]/sin^3(x).
</span>
<span>If we multiply the LHS by [1 + cos(x)]/[1 + cos(x)], we get:
LHS = csc(x)/[1 - cos(x)]
= {csc(x)[1 + cos(x)]/{[1 + cos(x)][1 - cos(x)]}
= {csc(x)[1 + cos(x)]}/[1 - cos^2(x)], via difference of squares
= {csc(x)[1 + cos(x)]}/sin^2(x), since sin^2(x) = 1 - cos^2(x).
</span>
<span>Then, since csc(x) = 1/sin(x):
LHS = {csc(x)[1 + cos(x)]}/sin^2(x)
= {[1 + cos(x)]/sin(x)}/sin^2(x)
= [1 + cos(x)]/sin^3(x)
= RHS.
</span>
<span>I hope this helps! </span>
To find the volume of this one we need to break it down
now i see half of a cylinder and rectangle:)
but first lets find the volume of the rectangle...
In order to find the Volume of a rectangle we need to use this formula...
Length x width x height
in this case...
length = 10in
width = 6 in
height = 8in
lets solve:)
10 x 6 x 8 = 480
or we write it like this
480in³
now time to find the volume of the half cylinder:)
But first lets remember the volume for a cylinder
Volume =

So lets find our measurements

= 3.14
r² = 5² or 25
h = 6
so lets plug in our values just like our formula said:)
3.14 x 25 x 6
now lets easily solve
<span>3.14 x 25 x 6 = 471
</span>now since we found an entire cylinder and we only want half of a cylinder lets divide our answer in half
471 ÷ 2 = 235.5
so we write it like this 235.5units³
But we have to add both of our multiples together so lets do that
Volume of rectangle = <span>480in³
</span>volume of half sphere = 235.5units³
480 + 235.5 = 715.5
answer = 715.5units³
I hope this helped and everyone learned something new
anyways don't forget to
MARK ME BRAINLIEST! :D
Well the solution to this problem is x < -4
Answer:
4 hours
Step-by-step explanation:
The speed of the first car is

While the speed of the second car is

The time it takes for each car to cover a distance d is

where
d = 960 km is the total distance covered
For car 1, the time taken is:

For car 2, the time taken is:

Therefore, the difference in time is:
