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If sin(2x) = 2sin(x)cos(x), what is the double angle formula for sine?

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Question: If sin(2x) = 2sin(x)cos(x), what is the double angle formula for sine?

Options:

  1. sin(2x) = sin(x) + cos(x)
  2. sin(2x) = 2sin(x)cos(x)
  3. sin(2x) = sin^2(x) - cos^2(x)
  4. sin(2x) = 2sin^2(x)

Correct Answer: sin(2x) = 2sin(x)cos(x)

Solution: 

The double angle formula for sine is sin(2x) = 2sin(x)cos(x).

If sin(2x) = 2sin(x)cos(x), what is the double angle formula for sine?

Practice Questions

Q1
If sin(2x) = 2sin(x)cos(x), what is the double angle formula for sine?
  1. sin(2x) = sin(x) + cos(x)
  2. sin(2x) = 2sin(x)cos(x)
  3. sin(2x) = sin^2(x) - cos^2(x)
  4. sin(2x) = 2sin^2(x)

Questions & Step-by-Step Solutions

If sin(2x) = 2sin(x)cos(x), what is the double angle formula for sine?
Correct Answer: sin(2x) = 2sin(x)cos(x)
  • Step 1: Understand what sin(2x) means. It represents the sine of double the angle x.
  • Step 2: Recognize that the equation given is sin(2x) = 2sin(x)cos(x).
  • Step 3: Identify that this equation is a formula that relates sin(2x) to sin(x) and cos(x).
  • Step 4: Conclude that this equation is known as the double angle formula for sine.
  • Double Angle Formula – The double angle formula for sine expresses sin(2x) in terms of sin(x) and cos(x).
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