İspat: - günah (7 teta) + günah (5 teta) / günah (7 teta) -sin (5 teta) =?
(sin7x + sin5x) / (sin7x-sin5x) = tan6x * cotx rarr (sin7x + sin5x) / (sin7x-sin5x) = (2sin ((7x + 5x) / 2) * cos ((7x5x) / 2) ) / (2sin ((7x-5x) / 2) * cos ((7x + 5x) / 2) = (sin6x * cosx) / (sinx * cos6x) = (tan6x) / tanx = tan6x * cottx
Şunu gösterin, (1 + cos teta + i * sin teta) ^ n + (1 + cos teta - i * sin teta) ^ n = 2 ^ (n + 1) * (cos teta / 2) ^ n * cos ( n * teta / 2)?
Lütfen aşağıya bakın. 1 + costheta + isintheta = r (cosalpha + isinalpha), burada r = sqrt ((1 + costheta) ^ 2 + sin ^ 2theta) = sqrt (2 + 2costheta) = sqrt (2 + 4cos ^ 2 (theta / 2) ) -2) = 2cos (theta / 2) ve tanalpha = sintheta / (1 + costheta) == (2sin (theta / 2) cos (theta / 2)) / (2cos ^ 2 (theta / 2)) = tan (theta / 2) veya alpha = theta / 2 sonra 1 + costheta-isintheta = r (cos (-alfa) + isin (-alfa)) = r (cosalpha-isinalpha) ve yazabiliriz (1 + costheta + isintta) ^ n + (1 + costheta-isintheta) ^ n, DE MOivre teoremini r ^ n (cosnalpha + isinnalpha + cosnalpha-isinnalpha) = 2r ^ ncosnalpha = 2 * 2 ^ ncos ^ n
Eğer günah teta + cos teta = p ise, p cinsinden günah ^ 2 teta + cos ^ 4theta nedir?
1 - ((p ^ 2-1) / 2) ^ 2 (sintheta + costheta) ^ 2 = 1 + 2sinthetacostheta = p ^ 2 yani sinthetacostheta = (p ^ 2-1) / 2 şimdi sin ^ 2theta + cos ^ 4theta = sin ^ 2theta + (1-sin ^ 2theta) cos ^ 2theta = 1-sin ^ 2thetacos ^ 2theta ve hepsini bir araya getirmek sin ^ 2theta + cos ^ 4theta = 1 - (((p ^ 2-1) / 2) ^ 2