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
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<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 reverse a percentage decrease you divide it by the decrease (+ 100%)
For example we will pick the number, 100, which is decreased by 15% to 85.
To make 85 back to 100 we divide it by the decrease (1-0.15):
85 / 0.85 = 100
To find out how much 85 increased to get back to 100, we do:
15 / 85 = 0.1765 = %17.65
15 is the reduction/difference, and 85 is the with reduction total.
Because percentages stay the same, this is applicable to any numbers, from this, we know that whenever something is reduced by 15% - when restored to it's original is increased by %17.65
The answer is %17.65
Answer:
8256
Step-by-step explanation:
Answer:11x + 5
Step-by-step explanation:1/3 times 9X is 3x. 1/3 times 15 is 5. Now you have 9x + 5 + 2x
9x + 2x = 11x
Final answer: 11x + 5
Answer:
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Step-by-step explanation:
