Question

If acos³θ + 3acosθsin²θ = m, a sin³θ + 3acos²θsinθ = n, prove that (m+n)^2/3 + (m-n)^2/3 = 2a^2/3.​​​

Answer 1

 (m+n)^2/3 + (m-n)^2/3 = 2a^2/3.

= (acos³θ + 3acosθsin²θ + a sin³θ + 3acos²θsinθ)^2/3 + (acos³θ + 3acosθsin²θ + a sin³θ + 3cos²θsinθ)^2/3

= a^2/3 (acos³θ + 3acosθsin²θ + a sin³θ + 3acos²θsinθ)^2/3 + a^2/3(acos³θ + 3acosθsin²θ + a sin³θ + 3acos²θsinθ)^2/3

Hence Proved.