# Factoring Trigonometric Expression

• February 18th 2013, 06:17 AM
vaironxxrd
Factoring Trigonometric Expression
Hello Everyone,
I have to factor the following expression and I can't figure out the proper procedures to do it (Headbang).

I'm assuming that I must take the difference of squares?

$\frac{1}{3} - \frac{2}{3}sin^2(x) + \frac{1}{3}sin^4(x)$
• February 18th 2013, 07:44 AM
BobP
Re: Factoring Trigonometric Expression
Remove the 1/3 as a common factor and then make use of $(a-1)^{2}\equiv a^{2} - 2a + 1$ followed by the trig identity $\sin ^{2}A + \cos^{2}A=1.$
• February 18th 2013, 08:15 AM
Plato
Re: Factoring Trigonometric Expression
Quote:

Originally Posted by vaironxxrd
I have to factor the following expression and I can't figure out the proper procedures to do it .
$\frac{1}{3} - \frac{2}{3}sin^2(x) + \frac{1}{3}sin^4(x)$

$\frac{1}{3} - \frac{2}{3}sin^2(x) + \frac{1}{3}sin^4(x)=\frac{(1-sin^2(x))^2}{3}$.
• February 18th 2013, 11:01 AM
vaironxxrd
Re: Factoring Trigonometric Expression
Quote:

Originally Posted by Plato
$\frac{1}{3} - \frac{2}{3}sin^2(x) + \frac{1}{3}sin^4(x)=\frac{(1-sin^2(x))^2}{3}$.

Plato is the following acceptable?

$\frac{1}{3} - \frac{2}{3}sin^2(x) + \frac{1}{3}sin^4(x) = \frac{1}{3}(1-2sin^2(x)+sin^4(x))$
• February 18th 2013, 11:08 AM
Plato
Re: Factoring Trigonometric Expression
Quote:

Originally Posted by vaironxxrd
Plato is the following acceptable?

$\frac{1}{3} - \frac{2}{3}sin^2(x) + \frac{1}{3}sin^4(x) = \frac{1}{3}(1-2sin^2(x)+sin^4(x))$

Acceptable to whom?

How would I know that answer to that?