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