1+ tan? 1- tan? 8 cos? u - sin?
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![Verify the identity.
\[
8 \left(\frac{1 + \tan^2 u}{1 - \tan^2 u}\right) = \frac{8}{\cos^2 u - \sin^2 u}
\]
Use a Reciprocal Identity, and simplify the compound fraction by multiplying by a common factor.
\[
8 \left(\frac{1 + \tan^2 u}{1 - \tan^2 u}\right) = 8 \left(1 + \frac{1}{\cos^2 u}\right) \times \frac{1}{1 - \frac{\sin^2 u}{\cos^2 u}}
\]
\[
= 8 \left(\frac{1}{\cos^2 u}\right) \left(\cos^2 u\right)
\]
\[
= 8 \left(\frac{1 - \frac{\sin^2 u}{\cos^2 u}}{\cos^2 u}\right) \left(\cos^2 u\right)
\]
\[
= 8 \left(\frac{1}{\cos^2 u} + \sin^2 u\right) \div \cos^2 u - \sin^2 u
\]
Use a Pythagorean Identity.
\[
= \square
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Transcribed Image Text:Verify the identity.
\[
8 \left(\frac{1 + \tan^2 u}{1 - \tan^2 u}\right) = \frac{8}{\cos^2 u - \sin^2 u}
\]
Use a Reciprocal Identity, and simplify the compound fraction by multiplying by a common factor.
\[
8 \left(\frac{1 + \tan^2 u}{1 - \tan^2 u}\right) = 8 \left(1 + \frac{1}{\cos^2 u}\right) \times \frac{1}{1 - \frac{\sin^2 u}{\cos^2 u}}
\]
\[
= 8 \left(\frac{1}{\cos^2 u}\right) \left(\cos^2 u\right)
\]
\[
= 8 \left(\frac{1 - \frac{\sin^2 u}{\cos^2 u}}{\cos^2 u}\right) \left(\cos^2 u\right)
\]
\[
= 8 \left(\frac{1}{\cos^2 u} + \sin^2 u\right) \div \cos^2 u - \sin^2 u
\]
Use a Pythagorean Identity.
\[
= \square
\]
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