Answer: -16/65
Step-by-step explanation:
Drawing the right triangle (as attached) gives us that 
Also, 
This means our original expression is equal to:
![\cos \left[\arcsin \left(\frac{12}{13} \right)+\arcsin \left(\frac{3}{5} \right) \right]](https://tex.z-dn.net/?f=%5Ccos%20%5Cleft%5B%5Carcsin%20%5Cleft%28%5Cfrac%7B12%7D%7B13%7D%20%5Cright%29%2B%5Carcsin%20%5Cleft%28%5Cfrac%7B3%7D%7B5%7D%20%5Cright%29%20%5Cright%5D)
Using the cosine addition formula, which states 
, we get this itself is equal to:
Since 
, we know that:
Similarly, cos(arcsin(3/5))=4/5.
This means the given expression is equal to:
8 · 7 = 56, therefore LCM(8, 56) = 56.
Recall the double/half angle formulas:
We're given 
, and since 
is between π/2 and π, we expect 
to be negative. So from the Pythagorean identity, we find
Also, we know 
will fall between π/4 and π/2, so both 
and 
will be positive. Then we find
and it follows that
Answer: D) (x+1)(x + 2)(x-3)
This is because the roots are x = -1, x = -2 and x = 3
Simply get all the numbers to each side to have 0 on the right side
x = -1 turns into x+1 = 0
x = -2 turns into x+2 = 0
x = 3 turns into x-3 = 0
The three factors are (x+1), (x+2) and (x-3)
Which leads to (x+1)(x+2)(x-3)
