Question 594548
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First off, "pie" is generally a food item, usually with a more or less flaky crust and either a sweet filling of some sort, often fruit, when it is served as a dessert item, or more of a savory filling when served as an entrée or side dish. "pi" is the commonly accepted Roman text representation of the 16th character of the lower case Greek alphabet *[tex \LARGE \left(\pi\right)] used in mathematics to represent the ratio between the circumference of a circle and its diameter.  Just sayin'


Use *[tex \LARGE \csc\varphi\ =\ \frac{1}{\sin\varphi}]


to write *[tex \LARGE 2\sin(x)\ -\ \csc(x)\ =\ 2\sin(x)\ -\ \frac{1}{\sin(x)}]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\sin(x)\ -\ \frac{1}{\sin(x)}\ =\ 0]


Multiply both sides by *[tex \LARGE \sin(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\sin^2(x)\ -\ 1\ =\ 0]


Add 1 to both sides and multiply by *[tex \small \frac{1}{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin^2(x)\ =\ \frac{1}{2}]


Take the square root


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin(x)\ =\ \pm\frac{\sqrt{2}}{2}]


On [*[tex \LARGE 0,2\pi])


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\pi}{4},\ \frac{3\pi}{4},\ \frac{5\pi}{4},\ \frac{7\pi}{4}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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