<span>Because the four numbers are consecutive, we can call the first one x, and the other three are x+1, x+2, and x+3, respectively.
x * (x+1) = (x+2) * (x+3) - 38
x^2 + x = x^2 + 5x +6-38
x^2 + x = x^2 + 5x - 32
-4x = -32
x=8
The four numbers are 8, 9, 10, and 11
check solution: 8*9=10*11-38
72=110-38
72=72</span>
Answer:
![\cos x=\dfrac{8}{f}](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cdfrac%7B8%7D%7Bf%7D)
Step-by-step explanation:
Given that,
![\tan x=\dfrac{e}{8}\\\\\sin x=\dfrac{e}{f}](https://tex.z-dn.net/?f=%5Ctan%20x%3D%5Cdfrac%7Be%7D%7B8%7D%5C%5C%5C%5C%5Csin%20x%3D%5Cdfrac%7Be%7D%7Bf%7D)
We need to find the value of cos x.
We know that,
![\tan\theta=\dfrac{\sin\theta}{\cos\theta}](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D)
Using the above relation,
![\dfrac{e}{8}=\dfrac{\dfrac{e}{f}}{\cos x}\\\\\cos x=\dfrac{\dfrac{e}{f}}{\dfrac{e}{8}}\\\\=\dfrac{e}{f}\times \dfrac{8}{e}\\\\=\dfrac{8}{f}](https://tex.z-dn.net/?f=%5Cdfrac%7Be%7D%7B8%7D%3D%5Cdfrac%7B%5Cdfrac%7Be%7D%7Bf%7D%7D%7B%5Ccos%20x%7D%5C%5C%5C%5C%5Ccos%20x%3D%5Cdfrac%7B%5Cdfrac%7Be%7D%7Bf%7D%7D%7B%5Cdfrac%7Be%7D%7B8%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7Be%7D%7Bf%7D%5Ctimes%20%5Cdfrac%7B8%7D%7Be%7D%5C%5C%5C%5C%3D%5Cdfrac%7B8%7D%7Bf%7D)
So, the value of cos x is equal to
.
Step-by-step explanation:
(2,4)===(4,-2)
(4,3)===(3,-4)
(2,3)===(3,-2)