Geometry
# Fundamental Trigonometric Identities

If $\tan \theta = \frac{ 2}{7}$, what is the value of

$\frac{ \cos \theta + 3 \sin \theta } { \cos \theta - 3 \sin \theta}?$

**Details and assumptions**

You may read up on Trigonometric Functions.

If

$\sum_{i=0} ^ {90} \cos ^2 i ^ \circ = \frac {a}{b},$

where $a$ and $b$ are positive coprime integers what is the value of $a+b$?

What is the value of:

$\left(1-\frac{1}{\cos 72 ^\circ}\right)\left(1+\frac{1}{\sin 18 ^\circ}\right)\left(1-\frac{1}{\sin 72 ^\circ}\right)\left(1+\frac{1}{\cos 18 ^\circ}\right)?$