Thread: can't seem to figure out how to verify this identity

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

for this one, first, i factored and got:

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

I don't know if the factoring helped or did anything, but I can't seem to get anything else to get 1.

Originally Posted by tennistudof2009

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

for this one, first, i factored and got:

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

I don't know if the factoring helped or did anything, but I can't seem to get anything else to get 1.

If you rewrite the problem as

maybe it is a bit clearer.

wow i did some totally unnecessary work...thanks a lot for your help!!!

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

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

1^2 = 1

1 = 1