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cos-x-cos-3x-cos-5x-2-1-sin-x-sin3x-sin-5x-1-tan-3x-




Question Number 204278 by liuxinnan last updated on 11/Feb/24
cos x+cos 3x+cos 5x=(√2)+1  sin x+sin3x+ sin 5x=1  tan 3x=?
$$\mathrm{cos}\:{x}+\mathrm{cos}\:\mathrm{3}{x}+\mathrm{cos}\:\mathrm{5}{x}=\sqrt{\mathrm{2}}+\mathrm{1} \\ $$$$\mathrm{sin}\:{x}+\mathrm{sin3}{x}+\:\mathrm{sin}\:\mathrm{5}{x}=\mathrm{1} \\ $$$$\mathrm{tan}\:\mathrm{3}{x}=? \\ $$
Commented by mr W last updated on 11/Feb/24
eq.(i) and eq.(ii) are not consistent.  ⇒no solution!
$${eq}.\left({i}\right)\:{and}\:{eq}.\left({ii}\right)\:{are}\:{not}\:{consistent}. \\ $$$$\Rightarrow{no}\:{solution}! \\ $$
Commented by liuxinnan last updated on 15/Feb/24
Commented by liuxinnan last updated on 15/Feb/24
It seems improper  Thank your tries
$${It}\:{seems}\:{improper} \\ $$$${Thank}\:{your}\:{tries} \\ $$
Answered by Frix last updated on 11/Feb/24
We had the same kind of problem before.  The mistake is similar to the very obvious  example:   { ((x=3)),((x=5)) :} ⇒^(???)  2x=8 ⇒ x=4  Or a less but still obvious:   { ((x^2 −x−6=0)),((x^2 −3x−4=0)) :} ⇒^(???)  2x−2=0 ⇒ x=1  Somehow people forget to test their solutions  lately...
$$\mathrm{We}\:\mathrm{had}\:\mathrm{the}\:\mathrm{same}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{problem}\:\mathrm{before}. \\ $$$$\mathrm{The}\:\mathrm{mistake}\:\mathrm{is}\:\mathrm{similar}\:\mathrm{to}\:\mathrm{the}\:\mathrm{very}\:\mathrm{obvious} \\ $$$$\mathrm{example}: \\ $$$$\begin{cases}{{x}=\mathrm{3}}\\{{x}=\mathrm{5}}\end{cases}\:\overset{???} {\Rightarrow}\:\mathrm{2}{x}=\mathrm{8}\:\Rightarrow\:{x}=\mathrm{4} \\ $$$$\mathrm{Or}\:\mathrm{a}\:\mathrm{less}\:\mathrm{but}\:\mathrm{still}\:\mathrm{obvious}: \\ $$$$\begin{cases}{{x}^{\mathrm{2}} −{x}−\mathrm{6}=\mathrm{0}}\\{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}=\mathrm{0}}\end{cases}\:\overset{???} {\Rightarrow}\:\mathrm{2}{x}−\mathrm{2}=\mathrm{0}\:\Rightarrow\:{x}=\mathrm{1} \\ $$$$\mathrm{Somehow}\:\mathrm{people}\:\mathrm{forget}\:\mathrm{to}\:\mathrm{test}\:\mathrm{their}\:\mathrm{solutions} \\ $$$$\mathrm{lately}… \\ $$

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