Question

What is the derivative of this function `(cos x) / (1-sinx)`?

Answer 1

`secx(secx+tanx).`

Explanation:

Let, `y=cosx/(1-sinx).`

`:. y=cosx/(1-sinx)xx(1+sinx)/(1+sinx),`

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

`:. y=(1+sinx)/cosx=1/cosx+sinx/cosx, i.e.,`

`y=secx+tanx.`

`rArr dy/dx=secxtanx+sec^2x=secx(tanx+secx).`