15. Solve the equation sin2x−2cosx=cos2x+2cosx+2 for x in the interval 0≤x≤2π. Then, write a general solution for this equation.
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Hello there,
My general solution differs from the one given by the textbook by not having a negative sign. Could anyone please explain why the textbook's general solution includes only solutions which lie to the right of x=43π?
Thank you.
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sin2x−2cosx=cos2x+2cosx+2
−2cos2x−22cosx−1=0
⇒cosx=2−2⇒x=43π
Therefore,
x=2nπ±43π
However, textbook gives:
x=2nπ+43π
----
Hello there,
My general solution differs from the one given by the textbook by not having a negative sign. Could anyone please explain why the textbook's general solution includes only solutions which lie to the right of x=43π?
Thank you.
----
sin2x−2cosx=cos2x+2cosx+2
−2cos2x−22cosx−1=0
⇒cosx=2−2⇒x=43π
Therefore,
x=2nπ±43π
However, textbook gives:
x=2nπ+43π