How do I prove that #(3-6 cos^2 x)/(sin x- cos x)# = 3(sin x + cos x)?
Yes, the equality is correct. See explanation.
On the numerator, factor out 3:
Remember the identity
Substitute the 1 in the numerator:
Simplify by adding the cos^2 x together:
Remember that when you have something of the form
So rewrite the numerator