Calculus

Solve the first-order initial value problem using half angle formulas

{y'(x)= 1 + sin^2 x
y (0)= -7

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  1. use the identity
    cos 2x = 1 - 2sin^2 x
    and solving for sin^2 x
    sin^2 x = 1/2 - (1/2)cos 2x

    then y'(x)= 1 + sin^2 x
    becomes
    y'(x)= 1 + sin^2 x
    becomes
    y'(x)= 1 + 1/2 - (1/2)cos 2x
    = 3/2 - (1/2)cos 2x

    this is now easy to integrate
    Don't forget to add the constant.

    plug in the point (0,-7) to find that constant.

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