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Which of these is an identity?

(A) #cotu=-sinu/cosu#
(B) #secu=-sin(1/u)#
(C) #cotu=1/tanu#
(D) #tan^2u+cot^2u=1#

Answer 1

Daniel Acosta

(A) #cotu=-sinu/cosu# is not an identity as #cotu=cosu/sinu# and not #-sinu/cosu#.

(B) #sec u=-sin(1/u)# too is not an identity as #secu=1/cosu#

(D) #tan^2u+cot^2u =1# is not an identity as #tan^2u=1/cot^2u#

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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.

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Which of these is an identity?

(A) #cotu=-sinu/cosu# (B) #secu=-sin(1/u)# (C) #cotu=1/tanu# (D) #tan^2u+cot^2u=1#

(A) #cotu=-sinu/cosu#
(B) #secu=-sin(1/u)#
(C) #cotu=1/tanu#
(D) #tan^2u+cot^2u=1#