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Back to 9.3 Double-Angle, Half-Angle, and Reduction Formulas

9.3 Exercise 17

Avg difficulty 2.5

We can determine the half-angle formula for tan( x 2 )= 1−cosx 1+cosx \tan \left(\frac{x}{2}\right) = \frac{\sqrt{1 - \cos x}}{\sqrt{1 + \cos x}} by dividing the formula for sin( x 2 ) \sin \left(\frac{x}{2}\right) by cos( x 2 ). \cos \left(\frac{x}{2}\right) . Explain how to determine two formulas for tan( x 2 ) \tan \left(\frac{x}{2}\right) that do not involve any square roots.

OpenStax Algebra and Trigonometry 2e, 9.3 Double-Angle, Half-Angle, and Reduction Formulas, exercise 17

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Adapted from College Algebra © 2021 Rice University. Licensed under CC BY 4.0. Sources: College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e, College Algebra with Corequisite Support 2e. Imported at revision 4922e46.