–sin2(x) = cos(2x) from [–π,π]

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If the equation is

- sin²(x) = cos(2x)

rewrite the left side using the Pythagorean identity,

sin²(x) = 1 - cos²(x)

and the right side using the double angle identity for cosine,

cos(2x) = 2 cos²(x) - 1

Then the equation transforms to

- (1 - cos²(x)) = 2 cos²(x) - 1

Solve for cos²(x) :

-1 + cos²(x) = 2 cos²(x) - 1

cos²(x) = 0

Take the square root of both sides to get

cos(x) = 0

Solve for x :

x = cos⁻¹(0) + 2nπ   or   x = cos⁻¹(0) - π + 2nπ

x = π/2 + 2nπ   or   x = -π/2 + 2nπ

where n is any integer. We get solutions in the interval [-π, π] when n = 0, giving the solutions

x = π/2   or   x = -π/2

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step-by-step explanation:

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.