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Verified Answer :

HomertheGenius

1 + cot² t = csc² t
\(1+cot ^{2} t = \frac{1}{sin ^{2} t} \\ 1+ \frac{cos^{2}t }{sin^{2}t } = \frac{1}{sin ^{2} t}\)  / * sin² t
sin² t + cos² t = 1
1 = 1
We have confirmed the identity.

The verification for the Pythagorean identity 1 + cot²∅ = cosec²∅ will lead to  sin²∅ + cos²∅ = 1

How to verify Pythagorean identity?

1 + cot²∅ = cosec²∅

Therefore,

cosec²∅ = 1 / sin²∅

cot²∅ = 1 / tan²∅ = cos²∅ / sin²∅

Hence,

1 + cos²∅ / sin²∅ =  1 / sin²∅

Therefore, multiply both sides by sin²∅

1(sin²∅) + (sin²∅) cos²∅ / sin²∅ = (sin²∅) 1 / sin²∅

sin²∅ + cos²∅ = 1

learn more on Pythagorean identity here: https://brainly.com/question/11674053

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