cotx=-sqrt3, cosx<0, tan(x-pi/6)

Question

cotx=-√3, cosx<0, tanx(x-Π/6)

find the exact value

Answer 1

cos x and cot x are both negative, so angle x is in the second quadrant.

 

cot^-1 -√3 = -π/6, so π-π/6 = 5π/6 is a solution.

 

Therefore the solution set is

 

{5π/6 + 2kπ | k ∈ Z}