Solve \sec(x)=\tan(x)I have been trying to do this problem:Solve\sec(x)=\tan(x),\ \ \

Adrien Barron

Adrien Barron

Answered question

2022-01-23

Solve sec(x)=tan(x)
I have been trying to do this problem: Solve sec(x)=tan(x),    0x<2π I started by rewriting sec(x)  as  1cos(x). I then rewrote tan(x)  to get  sin(x)cos(x) Therefore: 1cosx=sinxcosx Therefore: 1=sinx,x=π2 However, this is not a solution to the original problem because both y=tan(x)  and  y=sec(x) have asymptotes as x=π2

Answer & Explanation

Brynn Ortiz

Brynn Ortiz

Beginner2022-01-24Added 12 answers

There is nothing wrong with what you did. The problem has no solution since, precisely, if xR is such that both tan(x)  and  sec(x) are defined, then sec(x)=tan(x)sin(x)=1. But at those numbers x for which sin(x)=1,tan(x)  and  sec(x) are undefined.

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