if cos(A - 3@)/cos^3@ = sin(A - 3@)/sin^3@ = m
the show that cos A = 2-m^2/m

First, use cos(A-3@)/cos3@ = m to tan3@ by simply expanding cos(A-3@).

Do the same using sin(A-3@)/sin3@ = m and then equate the two.

This way @ is eliminated and you will get the desired result.

Thanks and Regards,
Deepak Kumar
AskIITians Faculty,
B. Tech, IIT Delhi.