Докажите тождество:1)cos^4t-sin^4t=cos2t2)cos^4t+sin^4t=1-(1/2)sin^2 * 2t

Question

Докажите тождество:
1)cos^4t-sin^4t=cos2t
2)cos^4t+sin^4t=1-(1/2)sin^2 * 2t

Answer 1

1+ (cos^4t+sin^2tcos^2t)/sin^2t=1/sin^2t 1+ cos^2t(cos^2t+sin^2t)/sin^2t=1/sin^2t 1+ cos^2t/sin^2t=1/sin^2t (cos^2t+sin^2t)/sin^2t =1/sin^2t 1/sin^2t =1/sin^2t 1=1 тождество доказано.