TITLE: How do I solve $\sqrt {1/2} = \cos (a)- \sin (a)?$
QUESTION [1 upvotes]: I have no idea how to do it...
I need to find $\alpha$ in this equation
$$\sqrt{1/2} = \cos(\alpha) - \sin(\alpha)$$
Thanks for your help

REPLY [0 votes]: $$\sqrt{1/2} = \cos(\alpha) - \sin(\alpha)$$
$${1/2} = \cos^2(\alpha) + \sin^2(\alpha) - 2\sin(\alpha)\cos(\alpha)  $$
$$(1/4) = \cos(\alpha)\sin(\alpha)$$
Substitute for variables, and solve the system of equations, and then solve the trig equation for $\alpha$ from $\cos(\alpha)$ and $\sin(\alpha)$ to get (Do these steps yourself; will be easier from here) :-
$$ \alpha = \pi \frac{24n-7}{12} ;  \alpha = \pi \frac{24n+1}{12}   $$
http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=bc455327d0772719486c1a3ecf2e96d3&title=Math%20Help%20Boards%3A%20Equation%20Solver&theme=blue
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