Докажите тождество: а) (sint-cost)²=1-sin2t; б) 2cos²t=1+cos2t

Question

Докажите тождество: а) (sint-cost)²=1-sin2t; б) 2cos²t=1+cos2t

Answer 1

А. (sint-cost)^2=1-sin2t
sin^2 t-2sin t cos t +cos^2t t=1-sin 2t
б. 2cos^2 t=1+cos2t
1+cos 2t=sin^2 t+cos^2 t-sin^2 t+cos^2 t=2 cos^2 t

Answer 2

А) (sint-cost)²=1-sin2t;
sin² t-2sin t cos t +cos²t t=1-sin 2t
б) 2cos²t=1+cos2t
1+cos 2t=sin² t+cos²t-sin² t+cos²t=2 cos² t

Comments

а. (sint-cost)^2=1-sin2t
sin^2 t-2sin t cos t +cos^2t t=1-sin 2t
б. 2cos^2 t=1+cos2t1+cos 2t=sin^2 t+cos^2 t-sin^2 t+cos^2 t=2 cos^2 t