Sin x/ 1+cos x + 1+cos x/sin x= 2cosec

[tex] \frac{sin x}{1+cos x} + \frac{1+cos x}{sin x} = 2cosec x[/tex]

[tex]\frac{(sin x)(sin x) + (1+cos x)(1+cos x)}{(1+cos x)(sin x)} [/tex]

[tex] \frac{sin² x + cos² x + 2cos x + 1}{(1+cos x)(sin x)} [/tex]

[tex] \frac{1 + 2cos x + 1}{(1+cos x)(sin x)}[/tex]

[tex] \frac{2 + 2 cos x}{(1+cos x)(sin x)} [/tex]

[tex] \frac{2(1+cos x)}{(1+cos x)(sin x)} [/tex]

[tex] \frac{2}{sin x} [/tex]

[tex]2 . cosec x[/tex]