Trig expression help pls

Question

zappy620 · Answer

$$\frac{ \sin^3\theta +\cos^3\theta}{ \sin \theta +\cos \theta }$$

xguardians · Answer

I know sin2 + cos2 = 1

zappy620 · Answer

The answer in the book is 
$$1 - \sin \theta \cos \theta$$

hero · Answer

Use the sum of cubes formula to factor. Hint: $\sin \theta + \cos \theta$ is a factor.

zappy620 · Answer

oh ok will try

hero · Answer

Good luck.

zappy620 · Answer

im stuck after getting
$$(\sin \theta - \cos \theta)(\sin/^2 \theta + \sin \theta \cos \theta +\cos^2 \theta)$$

hero · Answer

$\sin\theta - \cos \theta$ is not a factor.

zappy620 · Answer

ops messed up on the writing but its sin^2 theta in the second group

zappy620 · Answer

did i use the sum of cubs wrong?

hero · Answer

Sum of Cubes Formula
$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$

zappy620 · Answer

oh so it wud be 
$$(\sin \theta + \cos \theta)(\sin^2+\sin \theta \cos \theta +\cos^2 \theta)$$

hero · Answer

$(\sin \theta + \cos \theta)(\sin^2-\sin \theta \cos \theta +\cos^2 \theta)$

zappy620 · Answer

assuming that's right, then i wud use this identity?
$$\sin^2 \theta + \cos^2 \theta = 1$$

zappy620 · Answer

oh thats where i get mixed up i guess

zappy620 · Answer

trying to attempt it again atm

hero · Answer

Yes, you can use that identity to simplify

hero · Answer

And don't forget to cancel any factors of one

zappy620 · Answer

so i'm confused on what to do next tbh

hero · Answer

Do you see any factor in the numerator that matches the expression in the denominator?

zappy620 · Answer

ohhh yea the 
$$\sin \theta + \cos \theta$$

hero · Answer

So you should have the correct result now.

zappy620 · Answer

yea ty so much

hero · Answer

yw

zappy620 · Answer

i was spending so long on it lol ty, have a good day :D

hero · Answer

Yep, almost everyone struggles with it at first. Then one day, it just clicks.

hero · Answer

What's funny about these is, tan, cot, sec, and csc can always be changed to some expression with sin and cos. Meanwhile, sin and cos can always be changed to x and y. So trig is nothing but glorified algebra.

hero · Answer

Even the most complicated expressions can be figured out.

hero · Answer

You should write that down and commit it to memory. You never know when you'll need to simplify a very complicated trig expression on a test.