Using the double angle identities, find sin2x given sinx=4/5

  24/25

Step-by-step explanation:

The usual form of the double-angle identity is for sine is ...

  sin(2x) = 2sin(x)cos(x)

The cosine can be found from the sine using the Pythagorean identity ...

  sin(x)² + cos(x)² = 1

  cos(x) = √(1 -sin(x)²)

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Filling in the given value for sin(x), we can find the cosine to be ...

  cos(x) = √(1 -(4/5)²) = √(9/25) = 3/5 . . . . . . . assuming a first-quadrant angle

Then the desired sine is ...

  sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5)

  sin(2x) = 24/25

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent

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