Question

ПОМОГИТЕ!!!!Упростить выражение:
а)(1-tg^2t)cos^2t

Answer 1

$a) (1 - tg^2 t)cos^2 t = (1 - frac{sin^2 t}{cos^2 t})cos^2 t =cos^2 t - sin^2 t = \\ = cos^2 t - (1 - cos^2 t)= cos^2 t - 1 + cos^2 t = 2cos^2 t - 1 = cos 2t$


$b) 2 cos^2(pi + frac{t}{4}) - 2 sin^2(pi + frac{t}{4}) = 2(2cos^2 (pi + frac{t}{4}) - 1)=\\= 2 cos(2pi + frac{t}{2}) = 2 cos(frac{t}{2})$