Geometry

# Tangent - Sum and Difference Formulas

Which of the following is equal to

$\frac{ \tan 43 ^ \circ - \tan 14 ^ \circ } { 1 + \tan 43 ^ \circ \times \tan 14 ^ \circ } ?$

Which of the following is equal to

$\frac{ \tan 19 ^ \circ + \tan 26 ^ \circ } { 1 - \tan 19 ^ \circ \times \tan 26 ^ \circ } ?$

If $\tan x=\frac{1}{14}$, the value of $\tan \left(x+\frac{\pi}{4}\right)$ can be expressed as $\frac{a}{b}$, where $a$ and $b$ are coprime positive integers. What is the value of $a+b$?

If $\tan N ^ \circ = \tan 12 ^ \circ + \sec 12 ^ \circ$, where $0 \leq N \leq 90$, what is the value of $N$?

Which of the following expressions is equal to $\tan 2 \theta$?

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