[latex] \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 [/latex]

[latex] \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 [/latex] [latex] \frac{tg^2q-1}{tg^2q+1}+\cos^2q= \frac{tg^2q-1+tg^2q\cos^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 [/latex]