Math 123 - College Trigonometry Euler’s Formula and ...

Pythagorean formula: cos 2(x) + sin (x) = 1 By the rule of exponent we know that e ix e = 1 However, using the Euler’s formula, we know eix = cos(x) + isin(x) and e ix = cos(x) isin(x) Hence, 1 = eix e ix = cos(x) + isin(x) cos(x) isin(x) = cos2(x) icos(x)sin(x) + icos(x)sin(x) i2 sin2(x) = cos 2(x) + sin (x) Therefore, cos 2(x) + sin (x) = 1. 1 ................
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