–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

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.