Answer:
Step-by-step explanation:
ITS THE THRID ONE!
Answer:
b6 2hich method
Step-by-step explanation:
I solv3 this
Answer:
![\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx%3D2%5Cpi%20k%2C%5C%20%5C%20k%5Cin%20Z%5C%5C%20%5C%5Cx%3D-%5Cdfrac%7B%5Cpi%20%7D%7B2%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z%5Cend%7Barray%7D%5Cright.)
Step-by-step explanation:
Given:
![\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1](https://tex.z-dn.net/?f=%5Csin%20%28x-90%5E%7B%5Ccirc%7D%29%2B%5Ccos%28x%2B270%5E%7B%5Ccirc%7D%29%3D-1)
First, note that
![\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x](https://tex.z-dn.net/?f=%5Csin%20%28x-90%5E%7B%5Ccirc%7D%29%3D-%5Ccos%20x%5C%5C%20%5C%5C%5Ccos%28x%2B270%5E%7B%5Ccirc%7D%29%3D%5Csin%20x)
So, the equation is
![-\cos x+\sin x= -1](https://tex.z-dn.net/?f=-%5Ccos%20x%2B%5Csin%20x%3D%20-1)
Multiply this equation by ![\frac{\sqrt{2}}{2}:](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3A)
![-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Ccos%20x%2B%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Csin%20x%3D%20-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%20%5C%5C%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Ccos%20x-%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Csin%20x%3D%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%20%5C%5C%5Ccos%2045%5E%7B%5Ccirc%7D%5Ccos%20x-%5Csin%2045%5E%7B%5Ccirc%7D%5Csin%20x%3D%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5C%5C%20%5C%5C%5Ccos%20%28x%2B45%5E%7B%5Ccirc%7D%29%3D%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
The general solution is
![x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.](https://tex.z-dn.net/?f=x%2B45%5E%7B%5Ccirc%7D%3D%5Cpm%20%5Carccos%20%5Cleft%28%5Cdfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Cright%29%2B2%5Cpi%20k%2C%5C%20%5C%20k%5Cin%20Z%5C%5C%20%5C%5Cx%2B%5Cdfrac%7B%5Cpi%20%7D%7B4%7D%3D%5Cpm%20%5Cdfrac%7B%5Cpi%20%7D%7B4%7D%2B2%5Cpi%20k%2C%5C%20%5C%20k%5Cin%20Z%5C%5C%20%5C%5Cx%3D-%5Cdfrac%7B%5Cpi%20%7D%7B4%7D%5Cpm%20%5Cdfrac%7B%5Cpi%20%7D%7B4%7D%2B2%5Cpi%20k%2C%5C%20%5C%20k%5Cin%20Z%5C%5C%20%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bl%7Dx%3D2%5Cpi%20k%2C%5C%20%5C%20k%5Cin%20Z%5C%5C%20%5C%5Cx%3D-%5Cdfrac%7B%5Cpi%20%7D%7B2%7D%2B2%5Cpi%20k%2C%5C%20k%5Cin%20Z%5Cend%7Barray%7D%5Cright.)
81 is a counter example of the conditional statement given.
81 has factors other than itself, 1 and the square root of 81 which is 9.
81 has factors of 3 and 27 which are not listed.