Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix D - Trigonometry - D Exercises - Page A32: 47


$(secy-cosy)=tany$ $siny$

Work Step by Step

Need to prove the identity $secy-cosy=tany$ $siny$ In order to prove this, take left side isolate. $secy-cosy=\frac{1}{cosy}-cosy$ $=\frac{1-cos^{2}y}{cosy}$ Since, ${1-cos^{2}y}=sin^{2}y$, Thus, $secy-cosy=\frac{sin^{2}y}{cosy}$ Now, $secy-cosy=\frac{siny}{cosy}\times$ $ siny$ Hence, $(secy-cosy)=tany$ $siny$
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