How to solve 2 sin 2 x + 3 sin x = 2 ?

Question

How to solve       2                  sin        2            x        +    3          sin      x        =    2  ?

gesogenqqp · Accepted Answer

f              (        x        )              =    2                  sin        2            x        +    3          sin      x        -    2    =    0  Replace   (  3  sin  ⁡  x  )   by   (  4  sin  ⁡  x  −  sin  ⁡  x  )  f  (  x  )  =  2      sin    2    ⁡  x  +  4  sin  ⁡  x  −  sin  ⁡  x  −  2  =  0By grouping, a factor  f  (  x  )  =  2  sin  ⁡  x  (  sin  ⁡  x  +  2  )  −  (  sin  ⁡  x  +  2  )  =  0  f  (  x  )  =  (  sin  ⁡  x  +  2  )  (  2  sin  ⁡  x  −  1  )  =  0We have 2 solutions:a.   sin  ⁡  x  =  −  2 (rejected since   &amp;lt;  −  1)b.             sin      x        =          1      2       The trig table and unit circle give 2 arcs x:      x    =          π      6       and       x    =                  5        π            6       that have same sine value             (              1        2            )      Answers for             (      0      ,      2      π      )      :            π      6                    and                            5        π            6

How to solve 2sin^2x+3sinx=2?

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