Question

Trigonometry prove that (m+n)^2/3+(m-n)^2/3=2p^2/3

Answer 1

m + n = acos3x + 3a cosx sin2x + asin3x + 3a cos2xsinx = a(sinx + cosx)3

(m + n)2/3 = a2/3 (sinx + cosx)2

m – n = acos3x + 3a cosx sin2x – asin3x – 3a cos2xsinx = a(cosx + sinx)3

(m – n)2/3 = a2/3 (cosx – sinx)2

(m + n)2/3 + (m – n)2/3 = a2/3 (sinx + cosx)2 + a2/3 (cosx – sinx)2 =

a2/3[(sinx + cosx)2 + (cosx – sinx)2] = 2a2/3