Math, asked by rakib89, 1 year ago

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

Answers

Answered by abhi569
2
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{<br />( height )^2 + ( base )^2= ( hypotenuse )^2}

= > cot²A + 1 = hypotenuse² / height²


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


Then,
= > cot²A + 1 cosec²A


Hence, proved.
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