`lim_(yto0) ((x+y)sec(x+y)-xsecx)/(y)` is equal to

Answer

A

Explanation

`underset(yto0)lim{(x{sec(x+y)-secx})/(y)+sec(x+y)}`
`=underset(yto0)lim[(x)/(y){(cosx-cos(x+y))/(cos(x+y)cosx)}]+underset(yto0)limsec(x+y)`
`=underset(yto0)lim[(x2sin(x+(y)/(2))sin((y)/(2)))/(ycos(x+y)cosx)]+secx`
`=underset(yto0)lim[(xsin(x+(y)/(2)))/(cos(x+y)cosx)xx(sin((y)/(2)))/((y)/(2))]+secx`
`=xtanxsecx+secx`
`=secx(xtanx+1)`