Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A 
Answer: 4.09
Step-by-step explanation:
25.7 divided by pie is 8.18 which is the diameter. divide that by 2 and u get the radius.
Answer:
2,995 or 35,940(?)
Step-by-step explanation:
I don't exactly remember how to do this so, I'll show you two different ways I solved this
Use the formula I=P*r*t
I=Interest
P=Principal
r=rate
t=time
To solve this you'll have to...
The principal is 29,950, the rate is 5% but it'll become a decimal which is 0.05, and the time is 2
Put it into the formula form 29,950*0.05*2= 2,995 in interest
Or...
You'll use the same formula, but this time multiply 0.05 by 12 since there are 12 months in one year which is 0.6, so...
29,950*0.6*2=35,940 in interest
I hope one works!
1/2 Gallon is equal to 64 ounces
16 x 6 = 96
96 + 64 = 160
5 gallons is equal to 640
640 - 160 = 480
Answer:
27 cubic in
Step-by-step explanation:
area of base (3x3) x height of the pyramid (3)