Trig Identities

[Snark]

This one is killing me. Seriously.

Prove this identity.

(sin^4x + 2sin^2x)(cos^2x + cos^4x) = 1

I decided to start by *on the LHS converting the cosines to sines

= (sin^4x + 2sin^2x)[1-sin^2x + (1-sin^2x)^2]

=(sin^4x + 2sin^2x)(1-sin^2x + 1 - sin^2x - sin^2x + sin^4x)

=(sin^4x + 2sin^2x)(-3sin^2x + sin^4x)

I really don't know what to do now. I'm not even sure if I started right, or if I made some calculation error in what I've done so far.

Help (and possibly some tips for a beginner) would be greatly (and I mean GREATLY) appreciated!

--Snark

 

[wjm11]

Prove this identity.
(sin^4x + 2sin^2x)(cos^2x + cos^4x) = 1

This is not an identity. It is not true for all x. (Try plugging in x=0 for example.)

I suggest you review your problem statement for accuracy.

 

[Snark]

I'm working straight out of a textbook (High School so all the identities are true). I put the parenthesis in the question for clarity (maybe I messed up the question ). Here is the question as written in the textbook.

Prove each identity.

sin^4 x + 2sin^2 x cos^2 x + cos^4 x = 1

***Edit
Major oops.

I think the question is supposed to be (sin^4 x) + (2sin^2 x cos^2 x) + (cos^4 x) = 1
Problem solved

Thanks wjm11 for pointing it out or I would have never noticed !

 

[Mrspi]

I'm working straight out of a textbook (High School so all the identities are true). I put the parenthesis in the question for clarity (maybe I messed up the question ). Here is the question as written in the textbook.

Prove each identity.

sin^4 x + 2sin^2 x cos^2 x + cos^4 x = 1

***Edit
Major oops.

I think the question is supposed to be (sin^4 x) + (2sin^2 x cos^2 x) + (cos^4 x) = 1
Problem solved

Thanks wjm11 for pointing it out or I would have never noticed !

Have you considered FACTORING the left side? Hint: think about the pattern for factoring a perfect square trinomial.

 

[Snark]

I'm working straight out of a textbook (High School so all the identities are true). I put the parenthesis in the question for clarity (maybe I messed up the question ). Here is the question as written in the textbook.

Prove each identity.

sin^4 x + 2sin^2 x cos^2 x + cos^4 x = 1

***Edit
Major oops.

I think the question is supposed to be (sin^4 x) + (2sin^2 x cos^2 x) + (cos^4 x) = 1
Problem solved

Thanks wjm11 for pointing it out or I would have never noticed !

Have you considered FACTORING the left side? Hint: think about the pattern for factoring a perfect square trinomial.

Yeah, I factored it as soon as I realised I was reading the question wrong, and it worked perfectly.
I guess I was expecting the questions to be harder than they really were so I saw them as such.

Thanks anyway!