Answer
$(a)$
$\csc t = \frac{1}{\sin t}$
$\sec t = \frac{1}{\cos t}$
$\cot t = \frac{1}{\tan t}$
$(b)$
$sin^2t+cos^2t=1$
$tan^2t+1=sec^2t$
$1+cot^2t=csc^2t$
Work Step by Step
These identities are true for any value of the variable $t$.
$(a)$ Reciprocal identities are :
$\csc t = \frac{1}{\sin t}$
$\sec t = \frac{1}{\cos t}$
$\cot t = \frac{1}{\tan t}$
$(b)$ Pythagorean identities are :
$sin^2t+cos^2t=1$
$tan^2t+1=sec^2t$
$1+cot^2t=csc^2t$
