Question

1.    If acos3Ɵ + 3acosƟsin2Ɵ = m, asin3Ɵ + 3acos2ƟsinƟ = n, prove that (m+n)2/3 + (m-n)2/3 = 2a2/3

Answer 1

Let θ=30°, then m=9a/4, n=a+3a/4=7a/4.

m+n=4a, m-n=a/2, (m+n)^⅔+(m-n)^⅔=a^⅔(4^⅔)+a^⅔(½^⅔)=3.15a^⅔≠2a^⅔.

Therefore, the proposition is not generally true for arbitrary θ.