(sec^4x - 2 sec^2x tan^2x + tan^4x) i need to simplify this equation and the answer is 1, i just dont know how 2 work it. Thx.
Hi Sundae,
I assume the expression you have is set to 0.
$\displaystyle \sec^4x-2\sec^2 x \tan^2 x+ \tan^4x=0$
Now factor:
$\displaystyle (\sec^2 x-\tan^2 x)^2=0$
Edit: No solution to the above equation, anyhow. So, you just want to simplify the expression. See my last post.
Ok sundae, now I understand.
$\displaystyle (\sec^2 x-\tan^2 x)^2$
$\displaystyle (\sec^2 x-\tan^2 x)(\sec^2 x-\tan^2 x)$
$\displaystyle \left(\frac{1}{\cos^2 x}-\frac{\sin^2 x}{\cos^2 x}\right)\left(\frac{1}{\cos^2 x}-\frac{\sin^2 x}{\cos^2 x}\right)$
$\displaystyle \left(\frac{1-\sin^2 x}{\cos^2 x}\right)\left(\frac{1-\sin^2 x}{\cos^2 x}\right)$
$\displaystyle \left(\frac{\cos ^2 x}{\cos^2 x}\right) \left(\frac{\cos ^2 x}{\cos^2 x}\right)=1$