Consider the left – hand side:

L.H.S. = sin θ (1 + tan θ) + cos θ (1+ cot θ)

= sin θ (1 + ) + cos θ (1+ )

= sin θ × (cos θ) ×

= (cos θ + sin θ)

= (cos θ + sin θ)

=

=

= cosec θ + sec θ

= R.H.S.

Hence, proved.