The German mathematician Karl Weierstrass (18151897) noticed that the substitution t
Chapter 7, Problem 59(choose chapter or problem)
The German mathematician Karl Weierstrass (18151897) noticed that the substitution t tansxy2d will convert any rational function of sin x and cos x into an ordinary rational function of t. (a) If t tansxy2d, 2 , x , , sketch a right triangle or use trigonometric identities to show that cosS x 2 D 1 s1 1 t 2 and sinS x 2 D t s1 1 t 2 (b) Show that cos x 1 2 t 2 1 1 t 2 and sin x 2t 1 1 t 2 (c) Show that dx 2 1 1 t 2 dt
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