## Calculus: Early Transcendentals 8th Edition

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