Question

(cos^3A-cos3A) /cosA + (sin^3A+sin3a)/sinA=3
Prove the above equation.

Answer 1

\[\large \cos(3A) =4\cos^3(A) - 3\cos(A)\]\[\large \sin(3A) = 3\sin(A) - 4\sin^3(A)\]

Answer 2

(cos^3A-cos3A) /cosA = (3cosA - 3cos^3A)/cosA = 3 -3cos^2A
(sin^3A+sin3a)/sinA = (3sinA - 3sin^2A)/sinA = 3 -3sin^2A
adding these we have
3+3 -3(cos^2A +sin^2A)