I can't figure this Trig Identity out help please?

[jtart2]

I need to verify the given identity. I've tried every which way i can think of, but can't figure this one out. I am self-studying this book "College Trigonometry 5th Edition by Aufmann.

This is exercise set 3.3, problem 63.

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

Can anyone figure this out, or is this a misprint?

Thanks for your help,

Joe

 

[Millennial]

Have you tried using the double angle formulae for cosine to expand the right hand side?

 

[uart]

Can anyone figure this out, or is this a misprint?

No Joe, it works out ok.

Start with $cos^2 x - sin^2 x = cos 2x$ and square both sides. This gets you the require RHS straight up and most of the terms you require on the LHS too. You then need to do a bit more work (apply more trig identities to the terms that don't yet "fit") on the LHS and it comes out fairly easily.

 

[jtart2]

Thanks, uart, I finally figured it out. I was starting on the left side instead of the right. After factoring and factoring and factoring it finally worked out! I've never factored so much in my life!

Joe