Notice that
• <em>π</em>/2 = <em>π</em>/3 + <em>π</em>/6
• <em>π</em>/6 = <em>π</em>/3 - <em>π</em>/6
Recall the angle sum identities for sine:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
sin(<em>x</em> - <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) - cos(<em>x</em>) sin(<em>y</em>)
By adding these together, we get
sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>) = 2 sin(<em>x</em>) cos(<em>y</em>)
==> sin(<em>x</em>) cos(<em>y</em>) = 1/2 (sin(<em>x</em> + <em>y</em>) + sin(<em>x</em> - <em>y</em>))
Now take <em>x</em> = <em>π</em>/3 and <em>y</em> = <em>π</em>/6 :
sin(<em>π</em>/3) cos(<em>π</em>/6) = 1/2 (sin(<em>π</em>/2) + sin(<em>π</em>/6))
So the blank should be filled with cos.
Answer:
13
Step-by-step explanation:
We can consider the complex number
as point with coordinates
where
is real part of the complex number and
is an imaginary part of the complex number.
The distance between two complex numbers is exactly tha distance between two points corresponding to each number.

Now find the distance between A and B:

Shifting down 4 means you are taking away 4.
F(x) = g(x) - 4 = 3x^2 - 4
Answer: 
Step-by-step explanation:
By the negative exponent rule, you have that:

By the exponents properties, you know that:

Therefore, you can rewrite the left side of the equation has following:

Descompose 32 and 8 into its prime factors:

Rewrite:

Then:

As the base are equal, then:

Solve for x:

Answer:
10
Step-by-step explanation:
3-(-2)+5
the negative signs next to each other combine to makes a (+)
3+2+5
then you just sum the up
=10