Question

How do you simplify the expression `sinx/cosx+cosx/(1+sinx)`?

Answer 1

`sec x`.

Explanation:

`"The Expression"=sin x/cos x + cos x/(1+sin x)`

`={(sin x)(1+sin x)+cos^2 x}/{(cos x)(1+sin x)}`

`=(sin x+sin^2 x+cos^2 x)/{(cos x)(1+sin x)}`

`=cancel(sin x+1)/(cos x cancel((1+sin x))`

`=1/cos x`

`=sec x`.