I am assuming you want to solve for x:-
Now cosec^2 2x = 1 - cot^2 2x so the equation becomes
3 cosec^2(2x) + 2 cosec 2x = cosec^2 2x
2 cosec^2 2x + 2 cosec 2x = 0
2 cosec 2x ( cosec 2x + 1) = 0
so 2 cosec 2x = 0 or cosec 2x = -1
cosec 2x = 0 or cosec 2x = -1
cosec 2x = 0 is indeterminate so we ignore the first one
cosec 2x = -1 can be written as 1 / sin 2x = -1
so sin 2x = -1
giving 2x = 270 degrees
Therefore x = 135 degrees answer
Answer:
20 cakes
Step-by-step explanation:
28/7=4 cakes per day
4x5= 20
20 cakes in 5 days
Hope it helps :)
Answer:
![\mathrm {7.1 \: inches}](https://tex.z-dn.net/?f=%5Cmathrm%20%7B7.1%20%5C%3A%20inches%7D)
Step-by-step explanation:
Circumference of a circle is ![\pi d](https://tex.z-dn.net/?f=%5Cpi%20d)
The diameter is
inches as shown in the readings of the scale.
![2.25\pi](https://tex.z-dn.net/?f=2.25%5Cpi)
![\approx 7.06858347058](https://tex.z-dn.net/?f=%5Capprox%207.06858347058)
Answer: Choice D) earns 5 times as many points compared to previous level
Reasoning:
Let's say she's at level x = 1. That means she earns y = 5^x = 5^1 = 5 points.
At level x = 2, she earns y = 5^x = 5^2 = 25 points
When x = 3, we have y = 5^x = 5^3 = 125 points
And so on. Each new level earns her 5 times as many points as the previous level.
Answer:
<em>Answer: choice D.</em>
Step-by-step explanation:
<u>Trigonometric Functions</u>
We need to recall some properties and definitions of the trigonometric functions.
![\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%20%5Ctheta%3D%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D)
![\displaystyle \sec \theta=\frac{1}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csec%20%5Ctheta%3D%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D)
We need to simplify the following expression:
![5\sin\theta\sec\theta](https://tex.z-dn.net/?f=5%5Csin%5Ctheta%5Csec%5Ctheta)
Substituting the identity for the secant:
![\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Csin%5Ctheta.%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D)
Operating:
![\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D)
Substituting the definition of the tangent:
![\displaystyle 5\sin\theta\sec\theta=5\tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Ctan%5Ctheta)
Correct choice D.