Solve for x: 6sin^2x+2sin^2x=1 fir – 90

Solve for x: 6sin^2x+2sin^2x=1 fir – 90<x<90​

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  1. Answer:

    Here we have the equation:

    6*sin²(x) + 2*sin²(x) = 1

    and we want to find a solution in the range:

    -90° < x < 90°

    First, we can take the sin²(x) as a common factor to get:

    6*sin²(x) + 2*sin²(x) = (6 + 2)*sin²(x) = 1

    8*sin²(x) = 1

    now we can divide both sides by 8

    sin²(x) = 1/8

    now we can apply the square root to both sides:

    √(sin²(x) = √(1/8)

    sin(x) = √(1/8)

    Now remember the inverse sine function, Asin(x)

    such that:

    Asin( sin(x) ) = sin( Asin(x) ) = x

    If we apply that to both sides, we get:

    Asin( sin(x) )  = Asin(√(1/8))

    x = Asin(√(1/8)) = 20.7°

    x = 20.7°

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