Question

sin^4(a)+cos^4(a)=3+cos4a/4 равны ли

Answer 1

Ответ: да.

Объяснение:

$sin^4alpha+cos^4alpha=sin^4alpha+2sin^2alphacos^2alpha+cos^4alpha-2sin^2alphacos^2alpha=\ \ =(sin^2alpha+cos^2alpha)^2-dfrac{1}{2}sin^22alpha=1-dfrac{1}{2}*dfrac{1+cos4alpha}{2}=dfrac{3+cos4alpha}{4}$