Find the general solution of equation \cot x+\tan x=2 My approach: \cot

Marla Payton 2021-12-30 Answered
Find the general solution of equation cotx+tanx=2
My approach:
cotx+tanx=(1+tan2x)tanx=2
sec2x+tanx=2
1(sinxcosx)=2
sin2x+cos2x=2sinxcosx
(sinxcosx)2=0
sinx=cosx
So, x=nπ+(π4). This was my answer. But the answer given is x=2nπ±π3
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Expert Answer

Ben Owens
Answered 2021-12-31 Author has 27 answers
You know that cot(x)=1tan(x). Take random letter, let a=tan(x)
Then it is
1a+a=2
1+a2=2a
a22a+1=0
(a1)2=0
a1=0
a=1
tan(x)=1
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servidopolisxv
Answered 2022-01-01 Author has 27 answers
wrong reduction to algebraic form.
tanxuu+1u=2u=1
u=1x=nπ+π4
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Vasquez
Answered 2022-01-09 Author has 460 answers

Note that it is enough to consider x>0. By AM-Gm inequality
cotx+tanx2cotxtanx=1
for all x{nπ2|nZ}Z and equality occur when
cotx=tanx
which implies x{nπ+π4|nZ}

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