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Question Number 41895 by lucha116 last updated on 15/Aug/18
3sin3x−cos3x+2sin9x4=4
Commented by MJS last updated on 15/Aug/18
theanswertothisquestionisincludedintheformersimilarone.therethemaximumwas(2π9+8π3z2)withz∈Z,hereit′sthezeros⇒x=2π9+8π3z
Answered by MrW3 last updated on 15/Aug/18
2(32sin3x−12cos3x)+2sin9x4=42(cosπ6sin3x−sinπ6cos3x)+2sin9x4=42sin(3x−π6)+2sin9x4=4sin(3x−π6)+sin9x4=2(1)sin(3x−π6)=1⇒3x−π6=2nπ+π2⇒x=23nπ+2π9...(i)(2)sin9x4=1⇒9x4=2mπ+π2⇒x=89mπ+2π9...(ii)sothat(i)and(ii)arethesame,23n=89mn=43m⇒m=3k⇒n=4ksolutionis:x=8k3π+2π9=(24k+2)π9withk=anyinteger
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