cos x+cos 3x+cos 5x=(√2)+1 sin x+sin3x+ sin 5x=1 tan 3x=?


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Question Number 204278 by liuxinnan last updated on 11/Feb/24

$\cos x + \cos 3 x + \cos 5 x = \sqrt{2} + 1$ $\sin x + \sin 3 x + \sin 5 x = 1$ $\tan 3 x = ?$
Commented by mr W last updated on 11/Feb/24

$e q . (i) a n d e q . (i i) a r e n o t c o n s i s t e n t .$ $\Rightarrow n o s o l u t i o n!$
Commented by liuxinnan last updated on 15/Feb/24

Commented by liuxinnan last updated on 15/Feb/24

$I t s e e m s i m p r o p e r$ $T h a n k y o u r t r i e s$
	Answered by Frix last updated on 11/Feb/24
	$We had the same kind of problem before. The mistake is similar to the very obvious example: { ((x=3)),((x=5)) :} ⇒^(???) 2x=8 ⇒ x=4 Or a less but still obvious: { ((x^2 −x−6=0)),((x^2 −3x−4=0)) :} ⇒^(???) 2x−2=0 ⇒ x=1 Somehow people forget to test their solutions lately...$
	$We had the same kind of problem before .$ $The mistake is similar to the very obvious$ $example :$ ${\begin{cases} x = 3 \\ x = 5 \end{cases} \overset{? ? ?}{\Rightarrow} 2 x = 8 \Rightarrow x = 4$ $Or a less but still obvious :$ ${\begin{cases} x^{2} - x - 6 = 0 \\ x^{2} - 3 x - 4 = 0 \end{cases} \overset{? ? ?}{\Rightarrow} 2 x - 2 = 0 \Rightarrow x = 1$ $Somehow people forget to test their solutions$ $lately . . .$
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