Respuestas

2013-12-04T01:02:42+01:00
2cotxsecx+2secx+cotx+1 = 0

Paso todo a seno y coseno:

cot x = cos x/sen x
sec x = 1/cos x


Quedaría:

2(cos x/sen x)(1/cos x) + 2(1/cos x) + (cos x/sen x) + 1 = 0

2cos x/sen x cos x + 2/cos x + (cos x/ sen x) = -1


2cos x cos x + sen x cos x * 2        
--------------------------------------------- + cos x/ sen x = -1
        sen x cos x


2(cos x)² + 2sen x cos x
------------------------------------ + cos x/ sen x = -1 
     sen x cos x


cos x(2cos x + 2sen x)
---------------------------------- + cos x/ sen x = -1 
    sen x cos x


2cos x + 2sen x      cos x       
------------------------ + ----------- = -1
      sen x               sen x


(2cos x + 2sen x)(sen x) + sen x cos x
--------------------------------------------------------- = -1
                   (sen x)²


2cos x sen x + 2(sen x)² + sen x cos x
--------------------------------------------------------- = -1
                  (sen x)²


sen x(2cos x + 2senx x + cos x)
----------------------------------------------- = -1
                (sen x)² 


2cos x + 2sen x + cos x
------------------------------------ = -1
            sen x


2cos x     2sen x     cos x
---------- + ----------- + --------- = -1
sen x       sen x      sen x 


2cos x           cos x
---------- + 2 + --------- = -1
sen x            sen x 


2cos x     cos x
---------- + --------- = -1-2
sen x      sen x 


2cos x     cos x
---------- + --------- = -3
sen x      sen x 


2cos x sen x + sen x cos x
---------------------------------------- = -3
          (sen x)²


3cos x sen x
------------------- = -3
  (sen x)²


3cos x/ sen x = -3  <--- cos x/ sen x = tan x

3tan x = -3

tan x = -3/3

tan x = -1

x = arctan -1

x = -45


Saludos desde Argentina.