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Solve $\frac{1-\sin y -\cos 2y}{\sin 2y-\cos y}=-1$ for $y$ without using a calculator
in Mathematics by Wooden Status (2,726 points) | 155 views

1 Answer

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First simplify LHS by applying double identities and factorization

[1-siny-(1-2siny^2)]/[2sinycosy-cosy]= -1

[-siny+2siny^2]/[2sinycosy-cosy]=-1

           siny(-1+2siny)/cosy(2siny-1)=-1

                          siny/cosy = -1

                               tany=-1

                                  y = 45 degrees, but tan is negative in 2nd and 4th quadrants:

                                 y= 180-45=135 degrees   or y= 360-45= 315 degrees
by Diamond (52,788 points)

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