1/1+tg^2a+1/1+ctg^2a=1

1 / (1 + tg^2α) + 1 / (1 + ctg^2α) = 1;

Применим основные формулы тригонометрии:

1 + (tgα) ^2 = 1 / (cosα) ^2 и 1 + (ctgα) ^2 = 1 / (sinα) ^2;

1 / (1 / (cosα) ^2) + 1 / (1 / (sinα) ^2) = 1;

1 * (cosα) ^2 + 1 * (sinα) ^2 = 1;

(cosα) ^2 + (sinα) ^2 = 1;

(sinα) ^2 + (cosα) ^2 = 1;

1=1;

Тождество доказано.