Question

How do you simplify `(sin(x)/(1+cos(x)))+(cos(x)/sin(x))`?

Answer 1

`1/sinx`

Explanation:

`(sinx/(1+cosx))+(cosx/sinx)`

=`(sinx*sinx+cosx*(1+cosx))/(sinx*(1+cosx)`

= `(sin^2x+cosx+cos^2x)/(sinx*(1+cosx)`

= `((1+cosx))/(sinx*(1+cosx)`

= `cancel((1+cosx))/(sinx*cancel(1+cosx)`

= `1/sinx`