Answer:
I got (1,2).
Step-by-step explanation:
Process of elimination:
Multiply the second equation by 3 to get same terms, subtract and solve for Y to get 2.
Plug 2 into second equation for Y to get x=1
(1,2)
Answer:
1 and 5 I think
Step-by-step explanation:
Answer:
<u>15</u>
<u>2x</u>
Step-by-step explanation:
Your question seems a bit incomplete, but for starters you can write
![\dfrac1{1-\sin x}-\dfrac{\sin x}{1+\sin x}=\dfrac{1+\sin x}{(1-\sin x)(1+\sin x)}-\dfrac{\sin x(1-\sin x)}{(1+\sin x)(1-\sin x)}=\dfrac{1+\sin x-\sin x(1-\sin x)}{(1-\sin x)(1+\sin x)}](https://tex.z-dn.net/?f=%5Cdfrac1%7B1-%5Csin%20x%7D-%5Cdfrac%7B%5Csin%20x%7D%7B1%2B%5Csin%20x%7D%3D%5Cdfrac%7B1%2B%5Csin%20x%7D%7B%281-%5Csin%20x%29%281%2B%5Csin%20x%29%7D-%5Cdfrac%7B%5Csin%20x%281-%5Csin%20x%29%7D%7B%281%2B%5Csin%20x%29%281-%5Csin%20x%29%7D%3D%5Cdfrac%7B1%2B%5Csin%20x-%5Csin%20x%281-%5Csin%20x%29%7D%7B%281-%5Csin%20x%29%281%2B%5Csin%20x%29%7D)
Expanding where necessary, recalling that
![(1-\sin x)(1+\sin x)=1-\sin^2x=\cos^2x](https://tex.z-dn.net/?f=%281-%5Csin%20x%29%281%2B%5Csin%20x%29%3D1-%5Csin%5E2x%3D%5Ccos%5E2x)
, you have
![\dfrac{1+\sin x-\sin x(1-\sin x)}{(1-\sin x)(1+\sin x)}=\dfrac{1+\sin x-\sin x+\sin^2x}{\cos^2x}=\dfrac{1+\sin^2x}{\cos^2x}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%2B%5Csin%20x-%5Csin%20x%281-%5Csin%20x%29%7D%7B%281-%5Csin%20x%29%281%2B%5Csin%20x%29%7D%3D%5Cdfrac%7B1%2B%5Csin%20x-%5Csin%20x%2B%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%3D%5Cdfrac%7B1%2B%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D)
and you can stop there, or continue to rewrite in terms of the reciprocal functions,
![\dfrac{1+\sin^2x}{\cos^2x}=\sec^2x+\tan^2x](https://tex.z-dn.net/?f=%5Cdfrac%7B1%2B%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%3D%5Csec%5E2x%2B%5Ctan%5E2x)
Now, since
![1+\tan^2x=\sec^2x](https://tex.z-dn.net/?f=1%2B%5Ctan%5E2x%3D%5Csec%5E2x)
, the final form could also take
![\sec^2x+\tan^2x=\sec^2x+(\sec^2x-1)=2\sec^2x-1](https://tex.z-dn.net/?f=%5Csec%5E2x%2B%5Ctan%5E2x%3D%5Csec%5E2x%2B%28%5Csec%5E2x-1%29%3D2%5Csec%5E2x-1)
or
She would need to score 16 correct answers, because 80/5 = 16.