Question

find the possible values of tanx,if cos2x+5sinx-cosx=3

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Solution:

Here, given in the question that

  cos2x+5sinxcosx=3

= 2cos^2x -1 +5sinxcos x  = 3     ( since, cos2x = 2cos^2x -1)

dividing both side by cos^2x we get

2 -1 +5tanx= 3sec^2x

1 + 5tanx =3(1+tan^2x)       ( since, sec^2x =1+tan^2x)

3+3tan^2x = 1+ 5tanx

3tan^2x -5tanx +2 =0

3tan^2x -3tanx -2tanx +2=0

3tanx(tan x -1) -2(tan x -1) =0

(3tanx -2) (tan x -1) =0

3tanx -2 =0  or tan x -1 =0

tan x = 2/3  or tan x = 1