Solve tan x + sec 2x = 1

EunoR 2020-11-24 Answered
Solve tanx+sec2x=1
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Expert Answer

hajavaF
Answered 2020-11-25 Author has 90 answers

When x=0:tan(0)+sec(20)=1 so x=0 is a solution, because tan(0)=0andcos(0)andsec(0)=1.
There is another solution at x=67.5 degrees. See below: If y=sin(x)ortan(x).cos(2x)=12sin2(x)=12y2,sec(2x)=112sin2(x),cos(x)=1y2.sin=opphyp=y1soadj=1y2.tan(x)=oppadj=y1y2.
Therefore, tan(x)+sec(2x)=y1y2+112y2=1.
y1y2=1112y2=12y2112y2=2y212y2.
y=0 is a solution (sin(x)=0sox=0)and:
11y2=2y12y2,
1y2=2y212y.
Squaring: 1y2=4y44y2+14y2,4y24y4=4y44y2+1,8y48y2+1=0.
So y2=(8±643216=12±24

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