Question

sin^3 x + cos^3 x over sinx + cosx =1-(sinx)(cosx) verify the Identities

Answer 1

well..this was asked before,but i can't find the question..so here goes:
\[a ^{3} + b ^{3} = (a+b)( a ^{2} -ab +b ^{2}\]

Answer 2

similiarly..\[\sin ^{3}x + \cos ^{3}x = (sinx +cosx)*(\sin ^{2}x -sinxcosx +\cos ^{2}\]

Answer 3

oops ... i forgot the closing brackets for both :)
you follow @Gabysolis49

Answer 4

I'm lost^

Answer 5

its just another way of writing it. if you simplify the rhs..you'l get the same thing okay?

Answer 6

\[\sin^3 x + \cos^3 x \over sinx + cosx\]

Answer 7

the hard part about this question is getting the idea to write the above.its all downhill from here :)

Answer 8

\[\sin3x+\cos3xsinx+cosx\] = \[1-(sinx)(cosx)\]

Answer 9

i cant seem to draaw the equation

Answer 10

Yea that's the equation

Answer 11

\[\sin^3 x + \cos^3 x \over sinx + cosx\] \[=1-(sinx)(cosx) \]

Answer 12

hey you guys..listen first

Answer 13

@aivantettet26 and @Gabysolis49 do you get how i changed the numerator??

Answer 14

we can divide sin^3x + cos^3x / sinx + cos x

Answer 15

okay? im listening XD

Answer 16

right check how i changed the numerator

Answer 17

okay okay. im following

Answer 18

Okay I just need help answering it ^^^

Answer 19

right here goes:

Answer 20

???^

Answer 21

\ (sinx +cosx)*(\sin ^{2}x -sinxcosx+\cos ^{2}x)\div(sinx +cosx)\]

Answer 22

oops

Answer 23

\[(sinx +cosx)*(\sin ^{2}x -sinxcosx+\cos ^{2}x)\div(sinx +cosx)\]

Answer 24

sorry guys..connection problems

Answer 25

@Gabysolis49 @aivantettet26

Answer 26

Okay continue please

Answer 27

i want u to do it now

Answer 28

see if you can cancel anything

Answer 29

Yea sinx and cosx

Answer 30

okay so write the new equation:

Answer 31

(Sinx+cosx)(sin^2 x+cos^2 x)

Answer 32

sorry..thats not it..try again :)

Answer 33

Sin^2 x-sinx cosx+cos^2 x

Answer 34

yah!

Answer 35

So how does that equal 1-sinx cosx

Answer 36

hmmm what is 1??? :)

Answer 37

@Gabysolis49

Answer 38

sin3x+cos3xsinx+cosx

=1−(sinx)(cosx)

Answer 39

sin^2x+cos^2x=1. you got it now ?