Question

Докажите тождество:
cos^4t+sin^4t=1-(1/2)sin^2 * 2t

Answer 1

$cos^4t+sin^4t=(cos^4t+2cos^2tsin^2t+sin^4t)-2cos^2tsin^2t=\=(sin^2t+cos^2t)^2-frac12(2cos tsin t)^2=1-frac12sin^22t$