Question

Proving Identities:
sin^3(x)+cos^3(x)+sin(x)cos^2(x)+sin^2(x)cos(x) = sin(x)+cos(x) ?
how?

Answer 1

Ooo monster. *looks*

Answer 2

maybe factor?

Answer 3

Its not equal.
http://www.wolframalpha.com/input/?i=sin%5E3%28x%29%2Bcos%5E3%28x%29%2Bsin%28x%29cos%5E2%28x%29%2Bsin%5E2%28x%29cos%5E2%28x%29%3Dsin%28x%29%2Bcos%28x%29

Answer 4

not equal? the book says prove the identities, it didn't say anything about it being an identity or not.
(_ _)"

Answer 5

Be kind of mean if the book gave you something that could not be proven, lol.

Answer 6

There must be a typo in it somewhere o.O

Answer 7

hmmm.

Answer 8

oh wait. there is.

Answer 9

Well, I didn't prove it BUT I did give up and just turn everything into a ton ton ton of sinx's.

Answer 10

lol. I was about to start manipulation, but I thought I would check just to make sure it was true.

Answer 11

i'm sorry. the last term on the left hand side, the cosx doesn't have to be squared.

Answer 12

so just sin^2(x)cosx?

Answer 13

yes sir.

Answer 14

Oh, well that one turns out just fine then :D

Answer 15

:) sorry for my mistake. so... how it can be proved?

Answer 16

Do this with the first two terms.

\[(\sin ^{2}x)(sinx) + (\cos ^{2}x)(cosx)\]
Now use the pythagorean identity on the sin^2(x) and the cos^2(x) in order to change the sin^2(x) into cosines and the cos^2(x) into sines

Answer 17

Use
\[\sin ^{2}x + \cos ^{2}x = 1\]
And solve for sin^2(x) in thefirst term and solve for cos^2(x) in the 2nd term. Then things will multiply and cancel out stuffz.

Answer 18

ok. (solving on paper)

Answer 19

done. :) thanks sir.

Answer 20

You could also use the fact that:\[s^3+c^3=(s+c)(s^2-sc+c^2)=(s+c)(1-sc)\]and:\[s^2c+sc^2=sc(s+c).\]Im using s for sin and c for cos because im lazy :P

Answer 21

See, you could've done that, but we ain't fancy folk D:

Answer 22

lolol.

Answer 23

(_ _) sorry because in my notebook both sin and cos are squared on the last term in the left hand side. but when I look at the book there goes the truth. sorry for disturbing you.

Answer 24

Textbooks make mistakes more often than we'd like.