# Math Help - verifying trigonometric identities

1. ## verifying trigonometric identities

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

2. Originally Posted by dmak263
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
$\frac{(sin^3(\alpha) + cos^3(\alpha))}{(sin(\alpha)+cos(\alpha))}$

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
-----------------------------------------
So the fraction becomes

$
\frac{(sin(\alpha) + cos(\alpha))(1-sin(\alpha)cos(\alpha))}{(sin(\alpha)+cos(\alpha)) }$

Now this =
$(1-sin(\alpha)cos(\alpha))$