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 
-- To play the six games, <span>Santiago Diaz Granados spent
(6 x 25) = 150 tokens.
-- As a result of his skill, experience, talent, steady hand, nerves
of steel, superior hand-eye coordination, and superb reflexes, </span><span>
Santiago Diaz Granados won</span>
(0 + 10 + 50 + 0 + 5 + 10) = 75 tokens.
-- At the end of the 6th game, <span>Santiago Diaz Granados was behind
the curve.
After spending 150 tokens and winning 75 tokens, </span><span>Santiago Diaz Granados
was down by (150 - 75) = 75 tokens since he arrived at the arcade.
Any true friend could look at the choices, could see that choice-B is
the correct one, and could advise </span><span>Santiago Diaz Granados to cash in
whatever he had left, accept his losses, return to his home, and live
to fight another day.
Viva </span><span>Santiago Diaz Granados ... </span><span>un verdadero héroe de su pueblo. Viva !</span>
The answers is C. because when you do 180/3-15 you get 45 as the answer.
Answer:
∠8 * 4 = ∠7 ----------------(1)
∠8 + ∠7 = 180 ------------(2)
Taking the value of ∠7 from (1) and using it in (2):
<u><em>∠7 = 4 * ∠8</em></u>
<u><em /></u>
∠8 + ∠7 = 180
∠8 + (4 * ∠8) = 180
∠8 + 4∠8 = 180
5∠8 = 180
∠8 = 36° ---------------(3)
Using the value of ∠8 from (3) in (2):
∠8 + ∠7 = 180
36 + ∠7 = 180
∠7 = 144° and ∠8 = 36°
Answer: The correct answer is B.
Step-by-step explanation: We are given the cost of restaurant meal of M. Clark is $25.50.
and she has given 20% of the meal's cost as a tip to the waiter.
Step 1: Calculating the amount of tip paid
Total tip paid = $5.1
Step 2: To find the total amount, we add the cost of the meal and the tip paid
Total amount = Cost of the meal + Tip paid
Total amount = $25.50 + $5.10
Total amount paid by Ms. Clark = $30.6
