ow to prove this trigonometric identity

Question

(1+tan(x))/(sin(x)+cos(x))=secx ??

Answer 1

The given trigonometric identity is (1+tan(x))/(sin(x)+cos(x))=secx

= (tan(x) + 1) / (sin(x) + cos(x))               [ since tanx= sinx/cosx ]

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

= [(sin(x) + cos(x))/cos(x)] / (sin(x) + cos(x))

= 1/cos(x)

= sec(x)

Hence it is proved.