Question

Tan x =-1by √3 lies in fourth quadrant then find cos x

Answer 1

Answer:

tan x = -1/$\sqrt{3}$

tan x = - tan (π/6)

tan x = tan (-π/6)        since tan (-θ) = - tan θ

for forth quadrant

tan ( 2π - θ ) =  - tan (θ)

so,

tan x = tan (2π - π/6)

tan x = tan ( 11 π / 6)

x = 11 π /6

cos x = cos ( 11 π /6)

cos x = cos ( 2π - π/6)

cos x = cos (π /6)      since cos (2π - θ) = cos θ

cos x = $\frac{\sqrt 3}{2}$