How do you find the general solution to the equation 6cos^2x-cosxsinx-sin^2x=0?

1 Answer
May 20, 2018

Solution: x in [0 , 2 pi),x ~~63.43^0 ,x~~ 108.43^0 and
x~~ 243.43^0 ,x~~ 288.43^0

Explanation:

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]