Answer:
multiplication property of one or identity
Step-by-step explanation:
Solution to equation
for all real values of x is
.
<u>Step-by-step explanation:</u>
Here we have ,
. Let's solve :
⇒ ![cosxtanx - 2 cos^2 x=-1](https://tex.z-dn.net/?f=cosxtanx%20-%202%20cos%5E2%20x%3D-1)
⇒ ![cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1](https://tex.z-dn.net/?f=cosx%28%5Cfrac%7Bsinx%7D%7Bcosx%7D%29%20-%202%20cos%5E2%20x%3D-1)
⇒ ![sinx = 2 cos^2 x-1](https://tex.z-dn.net/?f=sinx%20%3D%202%20cos%5E2%20x-1)
⇒ ![sinx = 2 (1-sin^2x)-1](https://tex.z-dn.net/?f=sinx%20%3D%202%20%281-sin%5E2x%29-1)
⇒ ![sinx = 1-2sin^2x](https://tex.z-dn.net/?f=sinx%20%3D%201-2sin%5E2x)
⇒ ![2sin^2x+sinx-1=0](https://tex.z-dn.net/?f=2sin%5E2x%2Bsinx-1%3D0)
By quadratic formula :
⇒ ![sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
⇒ ![sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B1%5E2-4%282%29%28-1%29%7D%20%7D%7B2%282%29%7D)
⇒ ![sinx = \frac{-1 \pm3}{4}](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B-1%20%5Cpm3%7D%7B4%7D)
⇒ ![sinx = \frac{1}{2} , sinx =-1](https://tex.z-dn.net/?f=sinx%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2C%20sinx%20%3D-1)
⇒ ![sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}](https://tex.z-dn.net/?f=sinx%20%3D%20sin%5Cfrac%7B%5Cpi%7D%7B6%7D%20%2C%20sinx%20%3D%20sin%5Cfrac%7B3%5Cpi%7D%7B2%7D)
⇒ ![x=\frac{\pi}{6} , x=\frac{3\pi}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D%20%2C%20x%3D%5Cfrac%7B3%5Cpi%7D%7B2%7D)
But at
we have equation undefined as
. Hence only solution is :
⇒ ![x=\frac{\pi}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B6%7D)
Since , ![sin(\pi -x)=sinx](https://tex.z-dn.net/?f=sin%28%5Cpi%20-x%29%3Dsinx)
⇒ ![x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}](https://tex.z-dn.net/?f=x%3D%5Cpi%20-%5Cfrac%7B%5Cpi%7D%7B6%7D%20%3D%20%5Cfrac%7B5%5Cpi%7D%7B6%7D)
Now , General Solution is given by :
⇒ ![x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}](https://tex.z-dn.net/?f=x%3D2k%5Cpi%20%2B%20%5Cfrac%7B%5Cpi%7D%7B6%7D%20%20%2C%20x%3D2k%5Cpi%20%2B%20%5Cfrac%7B5%5Cpi%7D%7B6%7D)
Therefore , Solution to equation
for all real values of x is
.
Hey there! :D
Let's break this up piece by piece.
The first two, let's say that the first boxes represent the bottom of the chart.
The first far left box would be 13.
The next one 9.
Going across, 10 and 11.
Two more up.
7 and 3.
One more across, which is 4.
So, 13, 9, 10, 11, 7, 3, 4 would be the ones you would want to shade.
I hope this helps!
~kaikers
Answer:
Step-by-step explanation:
is -7