Calculus 8th Edition

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

Appendix D - Trigonometry - D Exercises - Page A32: 50


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

Work Step by Step

Need to solve the identity $2$ $csc$ $2t=sec$ $t$ $csc$ $t$ In order to prove this, take left side isolate. $2$ $csc$ $2t=\frac{2}{sin2t}$ 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 $\frac{1}{cost}=sec$ Therefore, $2$ $csc$ $2t=csct$ $sect$ Hence, $2$ $csc$ $2t=sec$ $t$ $csc$ $t$
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