First, notice that:
![2\tan (\frac{x}{2})=2\cdot(\pm\sqrt[]{\frac{1-cosx}{1+\cos x})}](https://tex.z-dn.net/?f=2%5Ctan%20%28%5Cfrac%7Bx%7D%7B2%7D%29%3D2%5Ccdot%28%5Cpm%5Csqrt%5B%5D%7B%5Cfrac%7B1-cosx%7D%7B1%2B%5Ccos%20x%7D%29%7D)
And in the denominator we have:

then, we have on the original expression:
![\begin{gathered} \frac{2\tan(\frac{x}{2})}{1+\tan^2(\frac{x}{2})}=\frac{2\cdot\pm\sqrt[]{\frac{1-\cos x}{1+cosx}}}{\frac{2}{1+\cos x}}=\frac{2\cdot(\pm\sqrt[]{1-cosx})\cdot(1+\cos x)}{2\cdot(\sqrt[]{1+cosx})} \\ =(\sqrt[]{1-\cos x})\cdot(\sqrt[]{1+\cos x})=\sqrt[]{(1-\cos x)(1+\cos x)} \\ =\sqrt[]{1-\cos^2x}=\sqrt[]{\sin^2x}=\sin x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B2%5Ctan%28%5Cfrac%7Bx%7D%7B2%7D%29%7D%7B1%2B%5Ctan%5E2%28%5Cfrac%7Bx%7D%7B2%7D%29%7D%3D%5Cfrac%7B2%5Ccdot%5Cpm%5Csqrt%5B%5D%7B%5Cfrac%7B1-%5Ccos%20x%7D%7B1%2Bcosx%7D%7D%7D%7B%5Cfrac%7B2%7D%7B1%2B%5Ccos%20x%7D%7D%3D%5Cfrac%7B2%5Ccdot%28%5Cpm%5Csqrt%5B%5D%7B1-cosx%7D%29%5Ccdot%281%2B%5Ccos%20x%29%7D%7B2%5Ccdot%28%5Csqrt%5B%5D%7B1%2Bcosx%7D%29%7D%20%5C%5C%20%3D%28%5Csqrt%5B%5D%7B1-%5Ccos%20x%7D%29%5Ccdot%28%5Csqrt%5B%5D%7B1%2B%5Ccos%20x%7D%29%3D%5Csqrt%5B%5D%7B%281-%5Ccos%20x%29%281%2B%5Ccos%20x%29%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B1-%5Ccos%5E2x%7D%3D%5Csqrt%5B%5D%7B%5Csin%5E2x%7D%3D%5Csin%20x%20%5Cend%7Bgathered%7D)
therefore, the identity equals to sinx
<span>Let n = the number of pages not read
Then the number of pages read = n/4 + 3
Since the total number of pages is 193, we have
n + n/4 + 3 = 193
5n/4 = 190
n = 152
At 8 pages per day it will take 152 pages/ 8 pages/day = 19 days
</span>
Answer: 
Step-by-step explanation:
A line that cuts a circle at two points is called "secant".
There is a theorem known as "Intersecting Secant Theorem". This is the theorem you need to use to find the value of "d".
According the Intersecting Secant Theorem:

Having this expression, the next step is to solve for "d":
Use Distributive property:

Subtract 256 from both sides:


Divide both sides by 16:

The value of "d" rounded to the nearest tenth is:

Answer:
The answer to your question is $ 8591.04
Step-by-step explanation:
Data
height = 11.4 m
diameter = 12 m
cost = $20/ft³
Process
1.- Calculate the volume of the cone
Formula
Volume = 1/3 πr²h
Substitution
Volume = 1/3 (3.14)(12/2)²(11.4)
Simplification
Volume = 1/3(1288.66)
Volume = 429.55 m³
2.- Calculate the cost
$20 ----------------- 1 m³
x ----------------- 429.55 m³
x = (429.55 x 20)/ 1
x = $ 8591.04
Answer:
The first table.
Step-by-step explanation:
A slope of 0 means that as x increases, y stays the same. In the first table, all of our y-values are 2; this means that y stays constant.
To prove it, we use our formula for slope:

The slope of the line between the first two points is
(2-2)/(-3--1) = 0/-2 = 0
The slope of the line between the second pair of points is
(2-2)/(-1-1) = 0/-2 = 0
The slope of the line between the next pair of points is
(2-2)/(1-3) = 0/-2 = 0
Since the slope between each pair of points is 0, the slope of the entire line is 0.