Can you help with trig?

Question

simplify (sin^3x + cos^3x) / sinx +cosx

Answer 1

use identity for a^3 + b^3
and (sinx)^2 + (cosx)^2 = 1

given expression
= { (sinx +cosx)[ (sinx)^2 -sinx cosx (cosx)^2] } / (sinx +cosx)

= [ (sinx)^2 -sinx cosx (cosx)^2]

= 1 - sinx cosx

Answer 2

1). Factor the numerator to get
(sin x + cos x)(sin²x -sin x cos x + cos² x)/(sin x + cos x).
Now, assuming, sin x + cos x isn't 0, we get
sin² x - sin x cos x + cos² x =
1 -(1/2) sin 2x.