Geometry
# Pythagorean Identities

$\large \dfrac { { \tan }^{ 2 }\theta }{ { \tan }^{ 2 }\theta+ 1 }= \, ?$

*Check out the set: 2016 Problems*

**True or False**:

$\large (\cos x - \sin x)(\cos x +\sin x) = \cos^4 x - \sin^4 x$

${\sin}\theta+{\sin}^2\theta= 1$

If the above equation is true, find the value of the expression below

${\cos}^2\theta+{\cos}^4\theta.$

Find the value of

$\cos^2 45^{\circ} +\sin^2 45^{\circ}.$