Geometry
Sum and Difference Trigonometric 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 \( \tan 2 \theta \)?