Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 5 - Trigonometric Identities - Section 5.2 Verifying Trigonometric Identities - 5.2 Exercises - Page 210: 100


$$\cos t=\sqrt{1-\sin^2t}$$ The equation is not an identity, which can be proved by trying $t=\pi$.

Work Step by Step

$$\cos t=\sqrt{1-\sin^2t}$$ To disprove this equation is an identity, we can take $t=\pi$. At $t=\pi$, $$\cos t=\cos\pi=-1$$ and $$\sqrt{1-\sin^2t}=\sqrt{1-\sin^2\pi}=\sqrt{1-0^2}=\sqrt1=1$$ As $-1\ne1$, at $t=\pi$, $\cos t\ne\sqrt{1-\sin^2t}$. The equation, therefore, is not an identity.
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