Question

sin^4(5x)+cos^4(5x)+2sin^2(5x)cos^2(5x)=1 prove or disprove. can someone help me with this?

Answer 1

Hint a^2+2ab+b^2=(a+b)^2

Answer 2

yes, and we know that:
\(\large\color{blue}{ \sin^4(5x)~~~=~~~ \left\{ \sin^2(5x) \right\}^2}\) and \(\large\color{blue}{ \cos^4(5x)~~~=~~~ \left\{ \cos^2(5x) \right\}^2}\)

Answer 3

yeah i did that and got stuck, let me post a pic of my notepad

Answer 4

can you show us what you got after doing that?

Answer 5

I mean, post any work till the point where you got stock. you can draw, type, use latex, or post screenshots.... whatever you prefer.

Answer 6

you forgot about the initial 2sin^2(5x)cos^2(5x)
that you had in your problem.

Answer 7

Oh no sin^4(x)+cos^4(x) doesn't equal one

Answer 8

Do you know how to factor a^4+2a^2b^2+b^4?

Answer 9

so then it equals (1-cos^2)^2 assuming where talking about sin^2

Answer 10

What your mistake is that:
you did \(\large\color{blue}{ \sin^4(5x)+\cos^4(5x)}\) correctly,
but...

you had, \(\large\color{blue}{ \sin^4(5x)+\cos^4(5x)\color{red}{+2\sin^2(5x)\cos^2(5x)}=1}\)

not just,
\(\large\color{blue}{ \cancel{ \sin^4(5x)+\cos^4(5x)=1}}\)

Answer 11

so then it equals (1-cos^2)^2 assuming where talking about sin^2

Answer 12

so what does the first two or three steps of the break down look like? cause im not sure what your saying?

Answer 13

Okay, looking at your equation you can see a \(\large\color{black}{ a^2+2ab+b^2 }\) right?
the confusing here is though, that it is disordered. \(\large\color{black}{ a^2+b^2+2ab}\)

Answer 14

See?

Answer 15

and i don't see how this would be factored

Answer 16

\(\large\color{black}{ (a+b)^2=a^2+2ab+b^2}\)

Answer 17

sin^2(5x) is a
cos^2(5x) is b

Answer 18

one more spoon, or you're good? :)

Answer 19

ok i got i think

Answer 20

okay, type your work.... or whatever you prefer..

Answer 21

i see the disorder now, cant believe i missed that

Answer 22

But the maun thing that you see it.... :)
So go for it:)

Answer 23

oops,, main, not maun. lol

Answer 24

thanks, is it ok if i ping you for any other questions i have? i working on a practice test