November 2004:
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| November 2004: | |
| Using the sum angle formula for cosines, namely cos(A-B) = cosA cosB + sinA sinB, derive the half-angle formula for cos(x/2) in terms of x. | |
| By the known identity, cos (x - x/2) = cos x cos (x/2) + sin x sin (x/2) Therefore, cos (x/2) = cos x cos (x/2) + sin x (1 - cos(x/2)2)1/2 Let A = cos(x/2). Hence, A = A cos x - sin x (1 - A2)1/2 By some algebra after squaring both sides, we get A2(1 - cos x)2 = sin2x (1-A2) Solving for A and applying the trigonometric identity cos2x + sin2x = 1, we obtain A = (+/-)(1 - cos x)1/2. Topic: Trigonometry
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