So, when we're tasked with things like this, rewriting everything in terms of sine and cosine and combining fractions often trivializes things, so doing just that gives us:
![\frac{\frac{1}{\cos{x}}-\frac{1}{\sin{x}}}{\frac{\cos{x}}{\sin{x}}-1}= \\\frac{\frac{=(\cos{x}-\sin{x})}{\cos{x}\sin{x}}}{\frac{\cos{x}}{\sin{x}}-\frac{\sin{x}}{\sin{x}}}=\\\frac{-(\cos{x}-\sin{x})}{\cos{x}\sin{x}}*\frac{\sin{x}}{\cos{x}-\sin{x}}=\\-\frac{1}{\cos{x}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Cfrac%7B1%7D%7B%5Ccos%7Bx%7D%7D-%5Cfrac%7B1%7D%7B%5Csin%7Bx%7D%7D%7D%7B%5Cfrac%7B%5Ccos%7Bx%7D%7D%7B%5Csin%7Bx%7D%7D-1%7D%3D%20%5C%5C%5Cfrac%7B%5Cfrac%7B%3D%28%5Ccos%7Bx%7D-%5Csin%7Bx%7D%29%7D%7B%5Ccos%7Bx%7D%5Csin%7Bx%7D%7D%7D%7B%5Cfrac%7B%5Ccos%7Bx%7D%7D%7B%5Csin%7Bx%7D%7D-%5Cfrac%7B%5Csin%7Bx%7D%7D%7B%5Csin%7Bx%7D%7D%7D%3D%5C%5C%5Cfrac%7B-%28%5Ccos%7Bx%7D-%5Csin%7Bx%7D%29%7D%7B%5Ccos%7Bx%7D%5Csin%7Bx%7D%7D%2A%5Cfrac%7B%5Csin%7Bx%7D%7D%7B%5Ccos%7Bx%7D-%5Csin%7Bx%7D%7D%3D%5C%5C-%5Cfrac%7B1%7D%7B%5Ccos%7Bx%7D%7D%20)
So out expression is 1/cos(x).
Answer:
![\large\boxed{t=0\ \vee\ t=\dfrac{1}{4}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bt%3D0%5C%20%5Cvee%5C%20t%3D%5Cdfrac%7B1%7D%7B4%7D%7D)
Step-by-step explanation:
![4t-16t^2=0\qquad\text{divide both sides by 4}\\\\\dfrac{4t}{4}-\dfrac{16t^2}{4}=\dfrac{0}{4}\\\\t-4t^2=0\\\\t(1-4t)=0\iff t=0\ \vee\ 1-4t=0\\\\1-4t=0\qquad\text{subtract 1 from both sides}\\\\-4t=-1\qquad\text{divide both sides by (-4)}\\\\t=\dfrac{1}{4}](https://tex.z-dn.net/?f=4t-16t%5E2%3D0%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%204%7D%5C%5C%5C%5C%5Cdfrac%7B4t%7D%7B4%7D-%5Cdfrac%7B16t%5E2%7D%7B4%7D%3D%5Cdfrac%7B0%7D%7B4%7D%5C%5C%5C%5Ct-4t%5E2%3D0%5C%5C%5C%5Ct%281-4t%29%3D0%5Ciff%20t%3D0%5C%20%5Cvee%5C%201-4t%3D0%5C%5C%5C%5C1-4t%3D0%5Cqquad%5Ctext%7Bsubtract%201%20from%20both%20sides%7D%5C%5C%5C%5C-4t%3D-1%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%20%28-4%29%7D%5C%5C%5C%5Ct%3D%5Cdfrac%7B1%7D%7B4%7D)
Answer:
i think 9
Step-by-step explanation:
45/5 is 9 so hope thus helps
Answer:
Step-by-step explanation:
Total cake shared=1/2
Pete share=x
Bill= twice as much as Pete
=2x
Pete's share+ Bill's share=total share
x+2x=1/2
3x=1/2
x=1/2÷3
x=1/2×1/3
=1/6
Pete's share=x=1/6
Bill's share=2x
=2(1/6)
=2/6
=1/3