first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.
let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so
![cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=cos%28%5Calpha%20%2B%20%5Cbeta%29%3D%20cos%28%5Calpha%29cos%28%5Cbeta%29-%20sin%28%5Calpha%29sin%28%5Cbeta%29%20%5C%5C%5C%5C%5C%5C%20cos%5Cleft%28%5Ccfrac%7B%5Ctheta%7D%7B2%7D%5Cright%29%3D%5Cpm%20%5Csqrt%7B%5Ccfrac%7B1%2Bcos%28%5Ctheta%29%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20cos%28135%5Eo%29%5Cimplies%20cos%2890%5Eo%2B45%5Eo%29%5Cimplies%20cos%2890%5Eo%29cos%2845%5Eo%29~~%20-%20~~sin%2890%5Eo%29sin%2845%5Eo%29%20%5C%5C%5C%5C%5C%5C%20%5Cleft%28%200%20%5Cright%29%5Cleft%28%20%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29~~%20-%20~~%5Cleft%28%201%5Cright%29%5Cleft%28%20%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%29%5Cimplies%20-%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
Using phytagoras rule your answer will be 63
Como no entiendo lo que es es eso ?
<u>Answer:</u>
The correct answer option is b. 1/216.
<u>Step-by-step explanation:</u>
The probability of getting a 4 when a die is rolled is 
which can be written as:
P (4) =
So to find the probability of getting a 4 each time if a die is rolled 3 times, we will multiply the probability of getting a 4 by 3.
P (getting a 4 each time when die is rolled 3 times) = 
= 1/216
