Question 966196
<pre>
{{{sin^4(x)+cos^4(x)}}}{{{""=""}}}{{{1-2sin^2(x)cos^2(x)}}}

(((sin^2(x)sin^2(x)+cos^2(x)cos^2(x)}}}

Substitute 1-cosē(x) for the second sinē(x) and
Substitute 1-sinē(x) for the first cosē(x)

(((sin^2(x)(1-cos^2(x))+(1-sin^2(x))cos^2(x)}}}

Distribute

{{{sin^2(x)-sin^2(x)+cos^2(x)-sin^2(x)cos^2(x)}}}

Rearrange and group terms:

{{{(sin^2(x)^""+cos^2(x))-sin^2(x)-sin^2(x)}}}

Substitute 1 for sinē(x)+cosē(x) and combine last two like terms.

{{{1-2sin^2(x)cos^2(x)}}}

Edwin</pre>