6 cos^2 x - cos x sin x - sin^2 x =0 or
sin^2 x +sin x cos x = 6 cos^2 x .Dividing by cos^2 x on
both sides we get, tan^2 x +tan x = 6 or
tan^2 x +tan x - 6 = 0 or
tan^2 x +3 tan x - 2 tan x - 6 = 0 or
tan x (tan x+3 )- 2 (tan x +3) = 0 or
(tan x+3 )(tan x- 2 ) = 0 :. either
(tan x+3 )=0 or (tan x- 2 ) = 0 :.
tan x =-3 :. x =tan^-1 (-3) ~~ -71.57^0 or 288.43^0 also
x = (180-71.57) ~~108.43^0
tan x = 2:. x =tan^-1 (2) ~~ 63.43^0 also
x = 180+63.43~~ 243.43^0
Solution: x in [0 , 2 pi),x ~~63.43^0 ,x~~ 108.43^0 and
x~~ 243.43^0 ,x~~ 288.43^0 [Ans]