prove with the help of geometry Cot^A=+1=cosec^A
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From Pythagoras theorem, we know : -
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
= > cot²A + 1 = hypotenuse² / height²
From trigonometric identities, we know hypotenuse²/ height² = cosec²∅
Then,
= > cot²A + 1 cosec²A
Hence, proved.
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
= > cot²A + 1 = hypotenuse² / height²
From trigonometric identities, we know hypotenuse²/ height² = cosec²∅
Then,
= > cot²A + 1 cosec²A
Hence, proved.
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