Top Ten Relations Between Sin and Cos

The Top Ten
1 (sin(x))^2 + (cos(x))^2 = 1
2 d/dx(sin(x)) = cos(x), d/dx(cos(x)) = -sin(x)
3 ∫cos(x) = sin(x), ∫sin(x) = -cos(x)
4 sin(x) / cos(x) = tan(x), cos(x) / sin(x) = cot(x)
5 sin(x) + sin(y) = 2 sin((x+y)/2) * sin((x-y)/2), cos(x) + cos(y) = 2 cos((x+y)/2) * cos((x-y)/2)
6 sin(x) - sin(y) = 2 cos((x+y)/2) * sin((x-y)/2)
7 cos(x) - cos(y) = -2 sin((x+y)/2) * sin((x-y)/2)
8 sin(θ) = cos(90 - θ), cos(θ) = sin(90 - θ)
9 cos(2x) = 1 - 2(sin(x))^2
10 sin(2x) = 2 sin(x) * cos(x)
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