The value of $cot^2 46° - sec^2 44° + (sin^2 1° + sin^2 3° + sin^2 5° + ... + sin^2 89°)$ is :

21.5

$cot^2 46° - sec^2 44° + (sin^2 1° + sin^2 3° + sin^2 5° + ... + sin^2 89°)$

Using :-

If sinA = cosB 

then  A + B = 90°

And  sin²A + sin²B  = 1   Iff A + B = 90° 

tan²44° - sec²44° + ( sin²1° + sin²3° + sin²5° + ......+ sin²89° )

From 1° tp 89° there are 88 angles excluding 45° .

so, Number of pairs = 22

{ we know,   sec²44° - tan²44° = 1 } 

= -1 + 22 + sin30°

= 21 + \(\frac{1}{2}\)

= 21.5