Question 172634
Prove the identity:
<pre><font size = 4 color = "indigo"><b>
{{{Sin(x)(1-2*Cos^2x+ Cos^4x) = Sin^5x}}}

Factor the expression in the parentheses:

{{{Sin(x)((1-Cos^2x)(1-Cos^2x)) = Sin^5x}}}

Write {{{(1-Cos^2x)(1-Cos^2x)}}} as {{{(1-Cos^2x)^2}}}

{{{Sin(x)(1-Cos^2x)^2 = Sin^5x}}}

Use the identity {{{Sin^2alpha+Cos^2alpha=1}}} as {{{1-Cos^2alpha=Sin^2alpha}}}

{{{Sin(x)(Sin^2x)^2 = Sin^5x}}}

{{{Sin(x)Sin^4x = Sin^5x}}}

{{{Sin^5x = Sin^5x}}}

Edwin</pre>