sec-2-1-o-sec-2-2-o-sec-2-3-o-sec-2-89-o-

Question Number 91689 by john santu last updated on 02/May/20

\sec^{2} 1^{o} + \sec^{2} 2^{o} + \sec^{2} 3^{o} + \dots + \sec^{2} 89^{o}

Commented by Prithwish Sen 1 last updated on 02/May/20

\sec^{2} a + {cose}^{2} a = \frac{\sin^{2} a + \cos^{2} a}{\sin^{2} a \cos^{2} a} = {cosec}^{2} a \sec^{2} a

Commented by Prithwish Sen 1 last updated on 02/May/20

\sec^{2} {1 cosec}^{2} 1 + \dots \dots \dots + \sec^{2} {44 cosec}^{2} 44 + 2

= 4 ({cosec}^{2} 2 + {cosec}^{2} 4 + \dots + {cosec}^{2} 88) + 2

= 16 ({cosec}^{2} 4 + {cosec}^{2} 8 + \dots + {cosec}^{2} 60 + \dots + {cosrc}^{2} 88) + 2

= 16 ({cosec}^{2} 2 + {cosec}^{2} 4 + \dots + {cosec}^{2} 42 + {cosec}^{2} 44) + 2

continue . .

Commented by jagoll last updated on 02/May/20

w h y \sec^{2} 1 cosec^{2} 1 ?

\sec^{2} 89 = cosec^{2} 1 \Rightarrow \sec^{2} 1 + \sec^{2} 89

= \sec^{2} 1 + cosec^{2} 1 s i r

Commented by jagoll last updated on 02/May/20

o o u h y e s . t h a n k y o u s i r

Commented by jagoll last updated on 02/May/20

b u t h o w t o g e t 4 \sin^{2} 2 ?

\sec^{2} 1 cosec^{2} 1 = \frac{4}{{(2 \sin 1 \cos 1)}^{2}} =

\frac{4}{\sin^{2} 2} = 4 cosec^{2} 2 s i r ?

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