[tex]\frac{cosec\theta+cotan\theta} {sec\theta+tan\theta}=\frac{cosec\theta+cotan\theta} {sec\theta+tan\theta}\times\frac{cosec\theta-cotan\theta}{cosec\theta-cotan\theta}\times\frac{sec\theta-tan\theta} {sec\theta-tan\theta}[/tex]
And use that,
[tex]\sec^2\theta-\tan^2\theta=1[/tex]
[tex]cosec^2\theta-cotan^2\theta=1[/tex]
