Solve \sin x+\cos x+\tan x+\csc x+\sec x+\cot x=-2 from 0<x<2\pi

kulisamilhh

kulisamilhh

Answered question

2022-04-21

Solve
sinx+cosx+tanx+cscx+secx+cotx=2
from 0<x<2π

Answer & Explanation

alastrimsmnr

alastrimsmnr

Beginner2022-04-22Added 18 answers

Substitute sinx+cosx=t
Also, t2=1+sin2x
Given reduces to :
sinx+cosx+sinxcosx+cosxsinx+1sinx+1cosx
=t+2t21+2tt21
t3t+2+2t=2t2+2
t3+2t2+t=0
t(t+1)2=0
Then it's all about solving a nice trigonometry equation. You can use:t2=sin(π4+x)

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