How do I solve this inequality? 3\sin(2x)> \sin(x)+\cos(x)+1

Madilyn Fitzgerald

Madilyn Fitzgerald

Answered question

2022-01-27

How do I solve this inequality? 3sin(2x)>sin(x)+cos(x)+1

Answer & Explanation

caoireoilns

caoireoilns

Beginner2022-01-28Added 12 answers

Hint
sinx+cosx=u,u2=1+sin2x
3(u21)>u+1
3u2u4>0
(3u4)(u+1)>0
  either  u>max(1,43)=?
or u<min(1,43)=?
Now keep in mind sinx+cosx=2sin(x+π4)2u2

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