Evaluate, sec ²10 ^o– cot ²80 ^o+ .

= sec ² (90° - 80°) – cot ² 80° +

= cosec ² 80° - cot ² 80° + (using that sin (90° - θ) = cos θ

and cos (90° - θ) = sin θ)

= 1 + (1/1)

(1 + cot ² θ = cosec ² θ and sin ² θ + cos ² θ = 1)

= 1 + 1

= 2

= R.H.S.