Cos a = 4/5 a принадлежит 4 степени. найти: sin2a, cos2s, tg2a, ctg2a

Вычислим:

cos (a) = 4 / 5; a € IV четверти;

sin (a) = √ {1 - [cos (a) ]^2};

sin (a) = √ {1 - 16 / 25} = 3 / 5;

sin (a) = - 3 / 5;

tg (a) = sin (a) / cos (a);

tg (a) = - 3 / 4;

sin (2 * a) = 2 * sin (a) * cos (a) = 2 * ( - 3 / 5) * 4 / 5 = - 24 / 25;

cos (2 * a) = 2 * [cos (a) ]^2 - 1 = (2 * 16 / 25) - 1 = 32 / 25 - 1 = 7 / 25;

tg (2 * a) = 2 * tg (a) / {1 - [tg (a) ]^2} = 2 * ( - 3 / 4) / (1 - 9 / 16) = ( - 3 / 2) / (7 / 16) = - 24 / 7;

ctg (2 * a) = 1 / tg (2 * a) = 1 / ( - 24 / 7) = - 7 / 24.