1. Докажите тождество: (1-cos^2t/1-sin^2t) + tgt*ctgt = 1/cos^2t

2. Известно, что sint = - 15/17, П

+5

1. (1 - cos^2t / 1-sin^2t) + tgt*ctgt = 1 / cos^2t

sin^2t / cos^2t + 1 = (sin^2t + cos^2t) / cos^2t = 1 / cos^2t

1/cos^2t = 1/cos^2t

2. sint = - 15/17

cos^2t = 1 - sin^2t = 1 - 225/289 = 64/289

cost = - 8/17

tgt = sint/cost

tgt = 15*17/17*8 = 15/8

ctgt = 1/tgt = 8/15