Consider the left – hand side:

L.H.S. =

= (sin²θ) + (1/sec² θ) (∵ 1 + tan² θ = sec² θ)

= (sin²θ) + (cos²θ) (∵ sin² θ + cos² θ = 1)

= 1

= R.H.S.

Hence, proved.