Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX D - Trigonometry - D Exercises - Page A 32: 50


$2$ $csc$ $2t=sec$ $t$ $csc$ $t$

Work Step by Step

We prove the identity $2$ $csc$ $2t=sec$ $t$ $csc$ $t$ $2$ $csc$ $2t=\frac{2}{sin2t}$ Since $sin2t=2sint$ $ cost$ $2$ $csc$ $2t=\frac{2}{2sintcost}$ $2$ $csc$ $2t=\frac{1}{sint}\times \frac{1}{cost}$ As $\frac{1}{sint}=csct$ and $\frac{1}{cost}=sect$ Therefore, $2$ $csc$ $2t=csct$ $sect$ Hence, $2$ $csc$ $2t=sec$ $t$ $csc$ $t$
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