Respuestas

2013-11-02T02:45:54+01:00
a) 1 – sen x = √3 cos x   b) 2 tan x csc x + 2 csc x + tan x + 1 = 0       Desarrollo:   a)    (1 – sen x)2 = (√3 cos x )2   (1 – sen x)2 = 3 cos2 x     (1 – sen x)2 = 3 (1 - sen2 x )   1 – 2sen x + sen2 x = 3 -sen2 x     -       2sen x + sen2 x + 3sen2 x = 3 – 1   4 sen2 x – 2sen x = 2   4 sen2 x – 2sen x – 2 = 0   (sen x – 1) (sen x +  ) = 0   Sen x -1 = 0               sen x +  = 0   Sen x  = 1                  sen x  =   X = sen-1(1)              X = sen-1()     X = 90o                    x = -30   Desarrollo:   b)    2 tan x csc x + 2 csc x + tan x + 1 = 0   (2 tan x csc x + 2 csc x) +( tan x + 1) = 0   2 csc x (tan x + 1) +( tan x + 1)   = 0   (tan x +1 ) (2csc x +1) = 0   tan x +1 = 0                      2csc x +1 = 0   tan x = -1                          2 csc = -1   x = tan-1 (-1)                     csc x =   x = -45o                               =                                                       -2 = sen x   Sen-1 (-2) = x    sen esta entre +1 y -1