Question

prove with the help of geometry Cot^A=+1=cosec^A

Answer 1

From Pythagoras theorem, we know : -

$( height )^2 + ( base )^2= ( hypotenuse )^2 \: \: \: \: \: \textit{...(i)}$



Now,
From trigonometric identities,
= > cotA = base / height


Square on both sides,
= > cot²A = base² / height²


Adding 1 on both sides,
= > cot²A + 1 = base² / height² + 1


= > cot²A + 1 = ( base² + height² ) / height²



$From \textit{ ( i )} \\ \mathsf{ ( height )^2 + ( base )^2= ( hypotenuse )^2}$

= > cot²A + 1 = hypotenuse² / height²


From trigonometric identities, we know hypotenuse²/ height² = cosec²∅


Then,
= > cot²A + 1 cosec²A


Hence, proved.