Question

cosec squared theta (1-cos squared theta) +sec squared theta (1-sin square theta) =2

Answer 1

use basic properties of trigonometric ratios.

Answer 2

We know,
sin²∅ + cos²∅ = 1
e.g sin²∅ = 1 - cos²∅
and cos²∅ = 1 - sin²∅
Use this here ,
Cosec²∅( 1 - cos²∅) + sec²∅( 1 - sin²∅)
= cosec²∅.sin²∅ + sec²∅ .cos²∅
= sin²∅/sin²∅ +cos²∅/cos²∅
= 1 + 1 = 2