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cos4α×tg2α-sin4α=-tg2α

$cos4alpha*tg2alpha-sin4alpha=-tg2alpha$
$frac{sin2alpha}{cos2alpha}*cos4alpha-sin4alpha=-frac{sin2alpha}{cos2alpha}$
$frac{cos4alpha*sin2alpha-cos2alpha*sin4alpha}{cos2alpha}=-frac{sin2alpha}{cos2alpha}$
$cos4alpha*sin2alpha-cos2alpha*sin4alpha=-sin2alpha$
$(frac{1}{2}(sin(4alpha+2alpha)-sin(4alpha-2alpha)))-(frac{1}{2}(sin(2alpha+4alpha)-sin(2alpha-4alpha)))$
$=-sin2alpha$
$(frac{1}{2}(sin6alpha-sin2alpha))-(frac{1}{2}(sin6alpha-sin(-2alpha)))=-sin2alpha$
$frac{sin6alpha-sin2alpha}{2}-frac{sin(-2alpha)-sin6alpha}{2}=-sin2alpha$
$frac{sin6alpha}{2}-frac{sin2alpha}{2}-frac{sin2alpha}{2}-frac{sin6alpha}{2}=-sin2alpha$
$-sin2alpha=-sin2alpha$