Докажите тождество sin^2t+tg^2t*sin^2t=tg^2t

Question

Докажите тождество sin^2t+tg^2t*sin^2t=tg^2t

Answer 1

Sin²t+tg²t*sin²t=tg²t

sin²t+tg²t*sin²2t=sin²t*(1+tg²t)=sin²t*(1/cos²t)=sin²t/cos²t=tg²t

tg²t=tg²t