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What identity is this? If it would be pythagorean identity the identity would change from csc squared to cot squared plus one

Answer 1

Pythagorean Identity

#csc^2theta= cot^2theta+1#

You can either state this is a pythagorean identity, or you can turn it into the any other pythagorean identity, for example: #sin^2theta+cos^2theta=1#

#csc^2theta= cot^2theta+1#

Multiply the given expression by #sin^2theta#

#sin^2theta(csc^2theta)= sin^2theta(cot^2theta+1)#

Apply reciprocal identity and quotient identity: #csctheta=1/sintheta# and #cottheta=costheta/sintheta#

#cancel(sin^2theta)(1/cancel(sin^2theta))= cancel(sin^2theta)*cos^2theta/cancel(sin^2theta)+1*sin^2theta#

#1= cos^2theta+sin^2theta#

Which is a pythagorean identity as well

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Answer 2

Samantha Abate

#1+cot^2x=csc^2x#

You have described the following Pythagorean identity relating the cosecant and cotangent:

#1+cot^2x=csc^2x#

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Answer 3

Zoe Austin

The identity you mentioned is the Pythagorean identity for cotangent:

[ \cot^2(\theta) + 1 = \csc^2(\theta) ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.