I am supposed to factor a trig expression.

the expression is:

1-2 sin^2x+sin^4x

Any help is appreciated!

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- Apr 18th 2009, 07:59 PMvrod guyFactoring
I am supposed to factor a trig expression.

the expression is:

1-2 sin^2x+sin^4x

Any help is appreciated! - Apr 18th 2009, 08:04 PMJhevon
note that your expression is a quadratic in $\displaystyle \sin^2 x$. to see this, let $\displaystyle a = \sin^2 x$, then your expression is

$\displaystyle 1 - 2a + a^2$

now hopefully you can factor that, then just replace $\displaystyle a$ with $\displaystyle \sin^2 x$ when done - Apr 19th 2009, 06:36 AMscottsw1
Jhevon,

When I factored, I came up with (1-sin^2x)^2=cos^4x. Is this correct? Vrod guy, I hope I was able to come up with the correct answer for you. - Apr 20th 2009, 06:09 PMvrod guy
Scott, Are you sure this is correct? Does anyone else agree with Scott?

- Apr 20th 2009, 06:24 PMProve It
Not if you were asked to factorise.

$\displaystyle 1 - 2a + a^2 = (1 - a)^2$

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

$\displaystyle = \left[(1 + \sin{x})(1 - \sin{x})\right]^2$.