If tanx=−1, and 90°<x<180°, find cos(x+30°).

Question

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Answer 1

x=-45°

so=135°

cos165°=-.965925.......

Answer 2

tan x = -1 implies that x = 45 + 90 = 135. (We added 90 because tan 45 = 1.)

cos(x+30) = cos(135 + 30) = cos(165)

165 degrees is in the 2nd quadrant, where cosine in negative.

cos(165) = cos(330/2)

cos(x/2) = +/- sqrt( (1 + cos(x)) / 2 )

cos(330/2) = - sqrt( (1+cos(330))/2)

cos(165) = - sqrt( (1 + sqrt(3)/2) / 2), ans.