<p>okay i know this is pretty simple but i still dont know how to do it</p>
<p>how do you go from (1-cos^2x)^3</p>
<p>to</p>
<p>(1-3cos^2x+3cos^4x-cos^6x)</p>
<p>i guess you could go like (1-cos^2x)(1-cos^2x)(1-cos^2x) and multiply it out but is ther a shortcut....like my teacher used pascals triabgle or something and i dunno how she did</p>
<p>Isnt this is a standard formula ? :unsure:</p>
<p>[a+b]^3 = a^3 - 3a^2xb + 3axb^2 - b^3</p>
<p>she probably used binomial expansion using the binomoial theorem and stuff</p>
<p>It seems strange to want to expand that, or maybe I'm reading it wrong.</p>
<p>sin^2(x) + cos^2(x) = 1</p>
<p>so 1-cos^2(x) = sin^2(x)</p>
<p>Then:</p>
<p>(1-cos^2(x))^3 = sin^6(x)</p>
<p>But that pascal's triangle thing you're mentioning is just the coefficients for the binomial expanision.</p>