Question

Simplify sin alpha /1+cos alpha +1+cos alpha /sin alpha

Answer 1

=sin^2 alpha+(1+cos^2 alpha)^2/

sin alpha (1+cos alpha)

=sin^2 alpha + 1+cos^2 alpha + 2cos alpha/

sin alpha(1+ cos alpha)

=(sin^2 alpha + cos^2 alpha) + 1+ 2cos alpha/

sin alpha (1 + cos alpha)

= 1+ 1 + 2cos alpha/

sin alpha(1 + cos alpha)

= 2+2cos alpha/

sin alpha(1 + cos alpha)

= 2 (1 + cos alpha)/

sin alpha (1 + cos alpha)

= 2/

sin alpha

= 2cosec alpha