Доказать тождество.(1+tg a) (1+ctg a)= ( 1/(sin a * cos a)) + a

Question

Доказать тождество.(1+tg a) (1+ctg a)= ( 1/(sin a * cos a)) + a

Answer 1

(1+tg a) (1+ctg a) = 1 + ctg a + tg a + ctg a * tg a = 1 + ctg a + tg a + 1 = = sin a/cos a + cos a/sin a + 2 = (sin^2 a + cos^2 a)/cos a sin a + 2 = (1/(sin a * cos a)) +2