Question 1169843
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin\varphi\ =\ \pm\sqrt{1\,-\,\cos^2\varphi]


Use that to calculate *[tex \Large \sin\alpha] and *[tex \Large \sin\beta].  Since the sine is positive in QI, select the positive roots.


Then using the values of *[tex \Large \cos\alpha] and *[tex \Large \cos\beta] with the values of *[tex \Large \sin] just calculated, calculate the values of 


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin\(\alpha\,+\,\beta\)\ =\ \sin\alpha\cos\beta\,+\,\cos\alpha\sin\beta]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos(\beta\,-\,\alpha)\ =\ \cos\beta\cos\alpha\ +\ \sin\beta\sin\alpha]


You get to do your own arithmetic.

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

From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> 
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