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Sum and Difference Trigonometric Formulas

These formulas explain how to add and subtract trigonometric functions (and their arguments). If you've got sum time, see what a difference these formulas will make for your trig toolkit.

Tangent - Sum and Difference

         

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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