Cos^2x+sin^2x * cos^2x-1=0

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To simplify this expression, we can first expand the second term in the expression using the identity:

cos^2(x) - 1 = -sin^2(x)

Now, the expression becomes:

cos^2(x) + sin^2(x) * (-sin^2(x)) = 0

cos^2(x) - sin^4(x) = 0

Now, we can use the Pythagorean identity:

cos^2(x) = 1 - sin^2(x)

Substitute this into the expression:

1 - sin^2(x) - sin^4(x) = 0

Rearranging and combining like terms:

-sin^4(x) - sin^2(x) + 1 = 0

This is a quadratic equation in sin^2(x), let t = sin^2(x), so we have:

-t^2 - t + 1 = 0

Solving this quadratic equation gives:

t = (1 ± √5) / -2

Since t = sin^2(x), we take the square roots of both sides to find the values of sin(x):

sin(x) = ± √((1 ± √5) / 2)

Therefore, the solutions of the original expression are sin(x) = ± √((1 ± √5) / 2)