6. Trigonometric Identities and More Equations
Double Angle Identities
Problem 5.18
Textbook Question
Textbook QuestionThe half-angle identity
tan A/2 = ± √[(1 - cosA)/(1 + cos A)]
can be used to find tan 22.5° = √(3 - 2√2), and the half-angle identity
tan A/2 = sin A/(1 + cos A)
can be used to find tan 22.5° = √2 - 1. Show that these answers are the same, without using a calculator. (Hint: If a > 0 and b > 0 and a² = b², then a = b.)
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