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tan^2(x) − 1 = 0

Guest Jun 1, 2017

Best Answer 

 #1
avatar+87301 
+2

 

 

tan^2 (x)  - 1  = 0     factor this as a difference of squares

 

[ tan x  - 1 ]  [ tan x  +  1  ]   = 0

 

Set each factor to 0   and solve for x

 

tan x  -  1   =   0      add 1 to both sides

 

tan x   =   1         and this occurs at    pi/4 +  pi*n   where n is an integer

 

And

 

tan x  +  1  = 0      subtract 1 from both sides

 

tan x  =  - 1      and this occurs at  (3pi)/4   +  pi*n    where n is an integer

 

 

cool cool cool

CPhill  Jun 1, 2017
 #1
avatar+87301 
+2
Best Answer

 

 

tan^2 (x)  - 1  = 0     factor this as a difference of squares

 

[ tan x  - 1 ]  [ tan x  +  1  ]   = 0

 

Set each factor to 0   and solve for x

 

tan x  -  1   =   0      add 1 to both sides

 

tan x   =   1         and this occurs at    pi/4 +  pi*n   where n is an integer

 

And

 

tan x  +  1  = 0      subtract 1 from both sides

 

tan x  =  - 1      and this occurs at  (3pi)/4   +  pi*n    where n is an integer

 

 

cool cool cool

CPhill  Jun 1, 2017

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