Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Test - Page 51: 30

Answer

Showed that given statement, $( 1- \sin\theta) ( 1+ \sin\theta)$ = $\cos^{2}\theta$, is an identity as left side transforms into right side.

Work Step by Step

Given statement is- $( 1- \sin\theta) ( 1+ \sin\theta)$ = $\cos^{2}\theta$ Left Side = $( 1- \sin\theta) ( 1+ \sin\theta)$ = $(1)^{2}$ - $(\sin\theta)^{2}$ [ We know that, $(a)^{2}$ - $(b)^{2}$ = $ ( a- b) ( a+ b) $] = $1 - \sin^{2}\theta$ = $\cos^{2}\theta$ [ From first Pythagorean identity, $ (1 - \cos^{2}\theta)$ can be written as $\sin^{2}\theta$] = Right Side i.e. Left Side transforms into Right Side i.e. Given statement, $( 1- \sin\theta) ( 1+ \sin\theta)$ = $\cos^{2}\theta$, is an identity.
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