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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.

# Triple Angle Identities

In the above diagram, the angle between $$y=ax$$ and the $$x$$-axis is $$\theta$$ and the angle between $$y=mx$$ and the $$x$$-axis is $$3\theta.$$ If $$a = \frac{1}{6},$$ what is the value of $$m?$$

If $$\sin \theta = \frac{1}{3},$$ what is $$\sin 3\theta?$$

What is $$6\times\left(\frac{3\times\tan10^{\circ}-\tan^3 10^{\circ}}{1-3\times\tan^2 10^{\circ}}\right)^2?$$

If $$\frac{\sin3\theta}{\cos3\theta+2\cos\theta}=7,$$ what is the value of $$\tan\theta?$$

If $$\frac{\sin3\theta}{\cos3\theta+2\cos\theta}=4,$$ what is the value of $$\tan\theta?$$

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