1 3/5 because 10 can go into 16 once and that leaves you with 6/10 and to simplify youd have to divinde by 2
Answer:
50% of 25 is 12.5 and 50% of 32 is 16
Step-by-step explanation:
25/2 = 12.5
32/2 = 16
Since
and
, we can rewrite the right side of the equation as
![\frac{1}{\sin^2{x}}-\frac{\cos^2{x}}{\sin^2{x}} =\frac{1-\cos^2{x}}{\sin^2{x}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%5Csin%5E2%7Bx%7D%7D-%5Cfrac%7B%5Ccos%5E2%7Bx%7D%7D%7B%5Csin%5E2%7Bx%7D%7D%20%3D%5Cfrac%7B1-%5Ccos%5E2%7Bx%7D%7D%7B%5Csin%5E2%7Bx%7D%7D%20%20)
Using the identity
, we can subtract
from either side to obtain the identity ![\sin^2{x}=1-\cos^2{x}](https://tex.z-dn.net/?f=%20%5Csin%5E2%7Bx%7D%3D1-%5Ccos%5E2%7Bx%7D%20)
substituting that into our previous expression, the right side of our equation simply becomes
![\frac{\sin^2{x}}{\sin^2{x}}=1](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Csin%5E2%7Bx%7D%7D%7B%5Csin%5E2%7Bx%7D%7D%3D1%20%20)
We can now write our whole equation as
![3\tan^2{x}-2=1](https://tex.z-dn.net/?f=%203%5Ctan%5E2%7Bx%7D-2%3D1%20)
Adding 2 to both sides:
![3\tan^2{x}=3](https://tex.z-dn.net/?f=%203%5Ctan%5E2%7Bx%7D%3D3%20)
dividing both sides by 3:
![\tan^2{x}=1](https://tex.z-dn.net/?f=%20%5Ctan%5E2%7Bx%7D%3D1%20)
![\tan{x}=\pm1](https://tex.z-dn.net/?f=%20%5Ctan%7Bx%7D%3D%5Cpm1%20)
When 0 ≤ x ≤ π, tan x can only be equal to 1 when sin x = cos x, which happens at x = π/4, and it can only be equal to -1 when -sin x = cos x, which happens at x = 3π/4