Question

sin^4 θ − cos^4 θ = sin^2 θ − cos^2 θ

asked to verify the identity

Answer 1

Hint:

x^4 - y^4 = (x^2)^2 - (y^2)^2

x^4 - y^4 = (x^2-y^2)(x^2+y^2)

Answer 2

not sure why he deleted all that, but he's right

Answer 3

haha, yea, me either.

Answer 4

so I say sin^4-cox^4=(sin^2)^2(cox^2)^2
and =(sin^2-cos^2)(sin^2+cos^2)
?

Answer 5

yes, then use the idea that sin^2+cos^2 = 1

Answer 6

ok

Answer 7

I'm assuming you meant to say sin^4-cox^4=(sin^2)^2 - (cox^2)^2

Answer 8

oh, yea

Answer 9

hmm, I'm not sure I see how to break that down to just sin^2 and cos^2

Answer 10

what do you mean

Answer 11

This type of thing is all about starting out with a good list of trig identities and seeing how few times you need to use it. The more times you do identities, the less you use the references. Eventually you just know them from using them so many times.

Answer 12

yea, I've been trying to memorize the learn the formulas well

Answer 13

I am thinking power reduction and/or sum and difference would be good ones to look at. Don't have the whole thing in my head yet, but from what I remember, I see those as a good start.

Answer 14

ok, Ill look into that also, thank you!

Answer 15

Now for sleep. I work in the morning... and have class in the afternoon. Whee! I hope what Jim and I pointed to leads somewhere good.

Answer 16

ohk lets start by solving the left hand side that is sin^4 d-cos^4 d (here 'd' is an angle just like theta tht u hv assumed in the ques)
alrt u must be knowing the identity a^2-b^2=(a+b)(a-b)
so sin^4 d -cos^4 d=(sin^2 d)^2 -(cos^2 d)^2
=[(sin^2 d)+(cos^2 d)][(sin^2 d)-(cos^2 d)]
since [(sin^2 d)+(cos^2 d)]=1
so ans is [(sin^2 d)-(cos^2 d)]
which is equal to the RHS :p
hence proved :)