Answer:
1
Step-by-step explanation:
Use the form for the factoring of the sum of cubes.
To make this easier to write, we'll use the substitutions ...
a = sin(θ), b = cos(θ)
It looks like you may want to simplify ...
(a³ +b³)/(a +b) +ab
= ((a +b)(a² -ab +b²))/(a +b) +ab
The factors of (a+b) cancel. In this case, we know that a² +b² = 1, so this becomes ...
= (1 -ab) +ab
= 1
The average of and
satisfies
Then
, so if
must be an integer, then the largest integer value it can take on is 19 if
can be a rational number (in which case
) or 18 if
must also be an integer.
Given that none of the provided answer choices lists 18 or 19, I'd bet there's a typo and you're supposed to find the maximum integer value of , in which case the answer would be B as the largest integer value would be 9.
