factor

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November 29th 2010, 03:30 PM
IDontunderstand

factor

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

I believe the answer is cos^4x

I want to say that 1-2(1+sin^2x)(sin^2x) if I move it around I get

I do not know where to go next or how it is cos^4x
November 29th 2010, 03:37 PM
dwsmith

Double angle formulas may help here
November 29th 2010, 03:39 PM
Archie Meade

Quote:

Originally Posted by IDontunderstand

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

I believe the answer is cos^4x

I want to say that 1-2(1+sin^2x)(sin^2x) if I move it around I get

I do not know where to go next or how it is cos^4x

As it says "factor" in your thread title...

$y=sin^2x$

and using $sin^2x+cos^2x=1\Rightarrow\ sin^2x=1-cos^2x$

$1-2y+y^2=(y-1)(y-1)=\left(sin^2x-1\right)\left(sin^2x-1\right)=\left(1-cos^2x-1\right)\left(1-cos^2x-1\right)$

which leads to the answer.
November 29th 2010, 03:51 PM
Soroban

Hello, IDontunderstand!

Quote:

$\text{Sinplifyt: }\:1-2\sin^2\!x+\sin^4\!x$

$\text{I believe the answer is: }\:\cos^4\!x$

Factor: . $1 - 2\sin^2\!x + \sin^4\!x \;=\;(\underbrace{1 - \sin^2\!x}_{\text{This is }\cos^2\!x})^2 \;=\;(\cos^2\!x)^2 \;=\;\cos^4\!x$

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