Question

$frac{cos alpha }{1+sin alpha } +tg alpha ; frac{tg ^{2}q-1 }{tg ^{2}q+1 } +cos ^{2}q ;frac{sinq+cos ^{3} alpha {} }{sin alpha +cos alpha } +sin alpha cos alpha$

Answer 1

$frac{cos alpha}{1+sin alpha} +tg alpha=frac{cos alpha}{1+sin alpha}+frac{sin alpha}{cos alpha}= frac{cos^2 alpha+sin alpha+sin^2 alpha}{(1+sin alpha)cos alpha}=\ frac{1+sin alpha}{(1+sin alpha)cos alpha}= frac{1}{cos alpha}=sec alpha$

$frac{tg^2q-1}{tg^2q+1}+cos^2q= frac{tg^2q-1+tg^2qcos^2q+cos^2q}{tg^2q+1}= frac{tg^2q-1+sin^2q+cos^2q}{tg^2q+1}= \frac{tg^2q-1+1}{tg^2q+1}= frac{tg^2q}{tg^2q+1}= frac{sin^2q}{cos^2q}*cos^2q=sin^2q$