Prove: cos⁡(x)/(1+sin⁡(x) )+(1+sin⁡(x))/cos⁡(x) =2sec⁡(x)

cos⁡(x)/(1+sin⁡(x) )+(1+sin⁡(x))/cos⁡(x) =2sec⁡(x)

Work on the left hand side.
[Common denominator is (1+sin(x))*cos(x)]
cos⁡(x)/(1+sin⁡(x) )+(1+sin⁡(x))/cos⁡(x)    
= (cos(x)^2+(1+sin(x))^2)/((1+sin(x))*cos(x))
=(cos(x)^2+1+sin(x)^2+2sin(x))/((1+sin(x))*cos(x))
=(cos(x)^2+sin(x)^2+1+2sin(x))/((1+sin(x))*cos(x))
=(1+1+2sin(x))/((1+sin(x))*cos(x))
=(2+2sin(x))/((1+sin(x))*cos(x))
=2(1+sin(x))/((1+sin(x))*cos(x))
=2/cos(x)
=2 sec(x)                [QED]