In Example 6, change the first term on the left to sin y/cos 3 y . Data
Question:
In Example 6, change the first term on the left to sin y/cos3 y .
Data from Example 6
Prove the identity
Because the more complicated side is on the left, we will change the left side to tan y, the form on the right. Because we want tan y as the final form, we will use the basic identities to introduce tan y where possible. Thus, noting the cot y in the denominator, we substitute 1/tan y for cot y. This gives
In the form on the right we now note the factor of tan y in each term. Factoring tan y from each of these terms, and then using the basic identity 1 + tan2 y = sec2 y in the form sec2 y − tan2 y = 1, we can complete the proof. Therefore,
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Related Book For
Basic Technical Mathematics
ISBN: 9780137529896
12th Edition
Authors: Allyn J. Washington, Richard Evans
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