Verify each identity:

1. (sin α-csc α) ² = cot²α-cos²α

2. 1-tan²A:1+tan²A=2cos²A-1

3. (cos α - sec α : sec α) + (sin α - csc α : csc α) = - 1

1.

(sin α - csc α) ²

= (sin α - 1/sin α) ²

= sin²α - 2 (sin α) (1/sin α) + 1/sin²α

= sin²α - 2 + 1/sin²α

= (sin²α - 1) + (1/sin²α - 1)

= - (1 - sin²α) + (1 - sin²α) / sin²α

= - cos²α + cos²/sin²α

= cot²α-cos²α

2.

(1-tan²A) / (1+tan²A)

= (1 - sin²A / cos²A) / (1 + sin²A/cos²A)

= (cos²A - sin²A) / (cos²A + sin²A)

= (cos²A - (1 - cos²A)) / (1)

= 2 cos²A - 1

3.

(cos α - sec α) / sec α + (sin α - csc α) / csc α

= (cos α - sec α) / sec α + (sin α - csc α) / csc α

= cos α/sec α - 1 + sin α / csc α - 1

= cos α / (1 / cos α) + sin α / (1 / sin α) - 2

= cos²α + sin²α - 2

= 1 - 2

= - 1