Question

Прошу упростите тригонометрическую функцию

cos4 α + cos²α * sin²α + sin²α

Answer 1

$cos 4alpha+cos^2alphasin^2alpha+sin^2alpha=cos4alpha+dfrac{1}{4}sin^22alpha+sin^2alpha=\ \ =cos4alpha+dfrac{1-cos4alpha}{8}+dfrac{1-cos2alpha}{2}=dfrac{7}{8}cos4alpha-dfrac{1}{2}cos2alpha+dfrac{5}{8}$