First, we need to know the smallest two digit prime number. It can't start with one, since one is not prime, so it must start with two (or be in the twenties.) 20 is divisible by 2, 4, 5, and 10, 21 is divisible by 7 and 3, 22 is divisible by 2 and 11, so the smallest prime number is 23.
Now we need the largest two-digit prime number. It cannot start with nine or eight, since both are composite, so it must start with seven (be in the seventies.) 79 is the largest integer in the seventies and also happens to be prime, so there's our largest two digit prime number.
now we just need to add them for the sum:
23+79=102
hope I helped, and let me know if you have any questions :D
Answer:
Step-by-step explanation:
Using the addition formulae for cosine
cos(x ± y) = cosxcosy ∓ sinxsiny
---------------------------------------------------------------
cos(120 + x) = cos120cosx - sin120sinx
= - cos60cosx - sin60sinx
= - 
cosx - 
sinx
squaring to obtain cos² (120 + x)
= 
cos²x + sinxcosx + 
sin²x
--------------------------------------------------------------------
cos(120 - x) = cos120cosx + sin120sinx
= -cos60cosx + sin60sinx
= - cosx + sinx
squaring to obtain cos²(120 - x)
= cos²x - sinxcosx + sin²x
--------------------------------------------------------------------------
Putting it all together
cos²x + cos²x + sinxcosx + sin²x + cos²x - sinxcosx + sin²x
= cos²x + cos²x + sin²x
= cos²x + sin²x
= (cos²x + sin²x) =
F(x) - g(x) =
x^1/2 - (2x^3 - x^1/2)=
x^1/2 - 2x^3 + x^1/2=
2x^1/2 - 2x^3
