доказать тождество (1-sin^2t)(1+tg^2t)=1

доказать тождество
(1-sin^2t)(1+tg^2t)=1

  • (1-sin^2t)(1+tan^2t)=1#10;cos^2 alpha +sin^2 alpha =1; cos^2 alpha =1-sin^2 alpha #10;cos^2t(1+ frac{sin^2t}{cos^2t} )=1#10;cos^2t+ frac{cos^2tsin^2t}{cos^2t} =1#10;cos^2t+ sin^2t=1
  • Формулы: sint + cost=1 --> 1-sint = cost tg t =sint/cost

    cost*(1+tgt)=1
    cost + cost*sint/ cost = 1
    cost+sint=1
    1=1