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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.

Half Angle Tangent Substitution

         

If \(\tan \frac{x}{2}=\frac{1}{4}\), the value of \(\cos x\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

If \( \tan \theta = t \), which of the following is equal to \( \tan 2 \theta \)?

If \(\tan \frac{x}{2}=-11\), the value of \(\tan x\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

If \( \tan \theta = t \), which of the following is equal to \( \cos 2 \theta \)?

If \(\tan x = 2\), then \(\sin 2x + \cos 2x + \tan 2x = -\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?

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