Question

докажите тождество
cos^4t + sin^4t= 1-12,sin^2 2t
фото буква б)

Answer 1

$1=sin^2t+cos^2t\\1=1^2=(sin^2t+cos^2t)^2=sin^4t+2sin^2tcos^2t+cos^4t=\\=(sin^4t+cos^4t)+2(sintcdot cost)^2=(sin^4t+cos^4t)+2(frac{1}{2}sin2t)^2=\\=(sin^4t+cos^4t)+frac{1}{2}sin^22t\\sin^4t+cos^4t=1-frac{1}{2}sin^22t$