Question

(cos(x)^3- sin(x)^3)/cos(x) - sin(x)

Answer 1

factor numerator as difference of two cubes

Answer 2

(cos(x)^2- sin(x)^2)

Answer 3

\[a^3-b^3=(a-b)(a^2+ab+b^2)\]

Answer 4

am i right satellite?

Answer 5

ok so how do I solve it after that

Answer 6

in your case you have
\[\frac{(\cos(x)-\sin(x))(\cos^2(x) +\cos(x)\sin(x)+\sin^2(x)}{\cos(x)-\sin(x)}\]

Answer 7

cancel to get
\[\cos^2(x)+\cos(x)\sin(x)+\sin^2(x)\]

Answer 8

and then use
\[\cos^2(x)+\sin^2(x)=1\] to get
\[1+\cos(x)\sin(x)\]

Answer 9

can I ask you anoth question

Answer 10

go ahead