165° = pi - 15° and sin(165°) = sin(15°) > 0, cos(165°) = -cos(15°) < 0.

Let's find sin and cos of 15°, 15° is a half of 30°. sin(30°) = 1/2, cos(30°) = sqrt(3)/2.

By the half-angle formulas(cos(15°))^2 = (1+cos(30°))/2 = (2+sqrt(3))/4,(sin(15°))^2 = (1-cos(30°))/2 = (2-sqrt(3))/4.

Socos(165°) = -cos(15°) = -sqrt(2+sqrt(3))/2,sin(165°) = sin(15°) = sqrt(2-sqrt(3))/2,tan(165°) = sin(165°)/cos(165°) = -sqrt(2-sqrt(3))/sqrt(2+sqrt(3)).

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