The general solution of tan(x)=tan(2x−pi/2)

Hayley Mcclain 2022-11-20 Answered
The general solution of tan ( x ) = tan ( 2 x π / 2 )
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Answers (2)

Savanna Smith
Answered 2022-11-21 Author has 17 answers
tan ( 2 x π 2 ) = tan ( π 2 2 x ) = 1 tan 2 x
tan x = 1 tan 2 x tan x tan 2 x = 1
tan x 2 tan x 1 tan 2 x = 1 2 tan 2 x = 1 + tan 2 x tan 2 x = 1 !
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Alberto Calhoun
Answered 2022-11-22 Author has 5 answers
If you set t = tan x and apply the duplication formula for the tangent, you have
tan ( 2 x π 2 ) = 1 tan 2 x = t 2 1 2 t ,
so the equation becomes
t 2 1 2 t = t t 2 1 = 2 t 2 t 2 = 1 ,
which has no real solution
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