Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
2. Verifying Trigonometric Identities
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Exercise 1 Page 362

Recall all of the Reciprocal Identities.

cot u

We are asked to fill in the blank to complete the following trigonometric identity. 1/tan u = Note that the left-hand side of the identity contains the reciprocal of a trigonometric function. This means that the given identity is one of the Reciprocal Identities. Let's recall all of the Reciprocal Identities.
Reciprocal Identities
sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u
csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u

Next, let's look for the identity that contains the expression 1tan u.

Reciprocal Identities
sin u = 1/csc u cos u = 1/sec u tan u = 1/cot u
csc u = 1/sin u sec u = 1/cos u cot u = 1/tan u

According to one of the identities from the table, 1tan u is equal to cot u. With this in mind, let's complete the given identity. 1/tan u = cot u