Timmy saved his money for a whole month. In week 1 he saved 10$. In week 2 he saved 15$. In week 3 he saved 8$. and in week 4 he
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Tom started with total 72 chocolate wafers.
<u><em>Explanation</em></u>
The number of chocolate wafers taken by 8 members of the baseball team are in the sequence :
The above sequence is <u>arithmetic sequence</u> with first term(a₁)= 1 and common difference (d) = 2
<u>Formula for Sum</u> of first terms in arithmetic sequence is....
So, the Sum of 8 terms in that sequence....
That means, the total number of chocolate wafers taken by the baseball team members is 64. Tom ate 5 and then gave his brother 3 chocolate wafers at first.
So, the total number of chocolate wafers at starting
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