Review the trigonometric Pythagorean identities listed below.

$\sin^2(x) + \cos^2(x) = 1$

$\tan^2(x) + 1 = \sec^2(x)$

$1 + \cot^2(x) = \csc^2(x)$

1. Use one of the equations to write a new expression for $\sin(x)$.

   Example (a):

   $\sin^2x = 1 − \cos^2x$

   $\text{sin}x=\pm \sqrt{1-\text{cos}^{2}x}$

2. Similarly, write a new expression for $\tan(x)$.

   Hint (b):

   Refer to part (a).

3. Similarly, write a new expression for $\cot^2(x)$.

   Hint (c):

   Refer to part (a).