1. Using Fundamental Identities
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We are asked to match each function with an equivalent expression.
Reciprocal Identities | ||
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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 identities that contain the expressions 1sec u, 1cot u, and 1csc 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 the first three identities, sin u = 1csc u, cos u = 1sec u, and tan u = 1cot u. With this in mind, we can match each of the functions labeled with (a), (b), and (c) with an equivalent expression.