Question

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

Answer 1

cos^4t+sin^4t=(cos^4t+cos^2t*sin^2t+sin^4t)-2cos^2t*sin^2t=(sin^2t+cos^2t)^2-1/2(2cost*sint)^2=1-1/2sin^2*2t