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

1. ## 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.

2. 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.
$\displaystyle \sin^4{x} + 2\sin^2{x}\cos^2{x} + \cos^4{x} = 1$

$\displaystyle (\sin^2{x} + cos^2{x})^2 = 1$

$\displaystyle (1)^2 = 1$

3. If you rewrite the problem as
$\displaystyle (\sin^2 x)^2 + 2\sin^2 x \cos^2 x + (\cos^2 x)^2 = 1$
maybe it is a bit clearer.

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

5. 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