Review the trigonometric Pythagorean identities from Chapter 1 Math Note listed below.

$\operatorname{sin}^2x +\operatorname{cos}^2x = 1$
$\operatorname{tan}^2x + 1 =\operatorname{sec}^2x$
$1 +\operatorname{cot}^2x =\operatorname{csc}^2x$

1. Use one of the equations to find a new expression for $\operatorname{sin}x$.

   Example (a):

    $\operatorname{sin}^2x = 1 − \operatorname{cos}^2x$

2. Similarly, write a new expression for $\operatorname{tan} x$.

   Hint (b):

   Refer to part (a).

3. Similarly, write a new expression for $\operatorname{cot}^2 x$.

   Hint (c):

   Refer to part (a).