Question 1045298
{{{sin^4(x) = (sin^2(x))^2}}}

= {{{(1-cos^2(x))^2 = 1 - 2cos^2(x) + (cos^2(x))^2}}}

= {{{1 - (1+cos2x) + ((1+cos2x)/2)^2}}}

= {{{-cos2x + (1+2cos2x +cos^2(2x))/4}}}

= {{{(1/4)(1-2cos2x+cos^2(2x))}}}

= {{{(1/4)(1-2cos2x+ (cos4x+1)/2)}}}

= {{{(1/4)(1/2)(2-4cos2x + cos4x +1)}}}

= {{{(1/8)(3 - 4cos2x + cos4x)}}}.