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lorraine2020

sin^4x-cos^4 x=2sin^2 x -1
prove.

Reply 1

username1732133

Original post by lorraine2020

sin^4x-cos^4 x=2sin^2 x -1
prove.

a^4-b^4 \equiv (a^2+b^2)(a^2-b^2)

Reply 2

thekidwhogames

LHS --> RHS
Start with LHS - you could factorise and then use identities you should know to simplify both brackets using the difference of squares. I think this is the easiest/shortest way to do it, especially if this is an A level question (this is probably what they expect too).

A slightly difference way to approach it:
If you want to prove a-b = c-d, this is the same as proving a-c+d=b of course. So proving one is eqv. to the other.

So proving sin^4(x) - cos^4(x) = 2sin^2(x) - 1 <==> proving sin^4(x) - 2sin^2(x) + 1 = cos^4(x).
This is quite easy to prove since you can factorise the LHS as (1-sin^2(x))^2, which of course is the RHS.