The value of $cot^2 46° - sec^2 44° + (sin^2 1° + sin^2 3° + sin^2 5° + ... + sin^2 89°)$ is :
Answer & explanation
Correct answer: option 4
$cot^2 46° - sec^2 44° + (sin^2 1° + sin^2 3° + sin^2 5° + ... + sin^2 89°)$
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