sin^2x (Power to Double Angle)
To find the formula for sin(2x) in terms of sin(x), we can use the double angle formula for sine
To find the formula for sin(2x) in terms of sin(x), we can use the double angle formula for sine.
The double angle formula for sine states that:
sin(2x) = 2sin(x)cos(x)
To derive this formula, we start with the addition formula for sine:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
Using this formula, we can substitute A = x and B = x:
sin(2x) = sin(x + x) = sin(x)cos(x) + cos(x)sin(x)
Since sin(x) is equal to sin(x) and cos(x) is equal to cos(x), we can simplify the equation to:
sin(2x) = 2sin(x)cos(x)
Therefore, the formula for sin(2x) in terms of sin(x) is 2sin(x)cos(x), which is the double angle formula for sine.
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