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sin-x-2a-3-a-1-How-many-a-that-can-satisfy-the-equation-above-




Question Number 18588 by Joel577 last updated on 25/Jul/17
sin x = ((2a + 3)/(a + 1))  How many a that can satisfy the  equation above?
sinx=2a+3a+1Howmanyathatcansatisfytheequationabove?
Answered by ajfour last updated on 25/Jul/17
−1≤((2a+3)/(a+1))≤1   ;  a≠−1  CaseI:  if a>−1  −a−1≤2a+3  and  2a+3≤a+1  ⇒      a≥−(4/3)  and  a≤−2  both cannot be true simultaneously  Case II:   a<−1  −a−1≥2a+3    and  2a+3≥a+1  ⇒    a≤−(4/3)   and  a≥−2  with  a<−1    ⇒      a ∈ [−2, −(4/3)] .
12a+3a+11;a1CaseI:ifa>1a12a+3and2a+3a+1a43anda2bothcannotbetruesimultaneouslyCaseII:a<1a12a+3and2a+3a+1a43anda2witha<1a[2,43].
Commented by Joel577 last updated on 25/Jul/17
thank you very much
thankyouverymuch

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