Question

cos a/1-sin a - cos a/1+sin a

Answer 1

$frac{cos a}{1-sin a}-frac{cos a}{1+sin a}=\\ frac{cos a(1+sin a)-cos a(1-sina )}{(1-sin a)(1+sin a)}=\\ frac{cos a+cos asin a-cos a+cos a sin a}{1^2-sin^2 a}=\\ frac{2cos a sina }{1-sin^2 a}=\\ frac{2 cos a sin a}{cos^2 a}=frac{2sina }{cos a}=2tg a$