MHB 8.aux.27 Simplify the trig expression

AI Thread Summary
The expression $\dfrac{{\cos 2x}}{{\cos x - \sin x}}$ simplifies to $\cos x + \sin x$, provided that $\cos x \neq \sin x$ to avoid division by zero. The simplification involves recognizing that $\cos 2x$ can be expressed as $\cos^2 x - \sin^2 x$, which factors into $(\cos x - \sin x)(\cos x + \sin x)$. The cancellation of $(\cos x - \sin x)$ is valid only when it is not equal to zero. This condition is crucial to ensure the expression remains defined.
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$\tiny{8.aux.27}$
Simplify the expression
$\dfrac{{\cos 2x\ }}{{\cos x-{\sin x\ }\ }}
=\dfrac{{{\cos}^2 x-{{\sin}^2 x\ }\ }}{{\cos x\ }-{\sin x\ }}
=\dfrac{({\cos x}-{\sin x})({\cos x}+{\sin x\ })}{{\cos x}-{\sin x}}
=\cos x +\sin x$

ok spent an hour just to get this and still not sure
suggestions?
 
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it's correct
 
With the proviso that we only use x s.t. [math]cos(x) \neq sin(x)[/math]. Since the reason for this has left the expression we need to state that.

-Dan
 
good point otherwise you get 0/0
 
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