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 
9514 1404 393
Answer:
20.8 cm
Step-by-step explanation:
The term "hypotenuse" suggests this triangle is a right triangle. Then the other leg can be found using the Pythagorean theorem:
x^2 +12^2 = 24^2
x^2 = 576 -144 = 432
x = √432 ≈ 20.8 . . . cm
The other leg is about 20.8 cm.
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<em>Additional comment</em>
A right triangle with a short leg that is 1/2 the length of the hypotenuse is the "special" 30°-60°-90° right triangle. The longer leg is √3 times the length of the short leg: 12√3 ≈ 20.8 cm.
Answer:
the volume is 
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cylinder.
Given data
Volume v = ?
Radius r = r in
Height h= 2r in
We are expected to solve for the volume of a cylinder, given the above data we can substitute it in the formula for volume of a cylinder to obtain our result
we know that the expression for the volume of a cylinder is
Hence the volume in terms of the radius is 
Answer:
about 61 mph
Step-by-step explanation:
