I've been trying to figure this out for hrs now, somebody please assist me.
sin^3 alpha + cos^3 aplha/ sin alpha + cos alpha = 1- sin alpha cos alpha
$\displaystyle \frac{(sin^3(\alpha) + cos^3(\alpha))}{(sin(\alpha)+cos(\alpha))}$
Remember that
a^3 +b^3 = (a+b)(a^2+b^2-ab)
Put a =sin(alpha) , b = cos(alpha)
Remembering that
sin^2(alpha)+cos^2(alpha) = 1
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So the fraction becomes
$\displaystyle
\frac{(sin(\alpha) + cos(\alpha))(1-sin(\alpha)cos(\alpha))}{(sin(\alpha)+cos(\alpha)) }$
Now this = $\displaystyle (1-sin(\alpha)cos(\alpha))$
Adarsh