Question

Prove that √(2√(2+2cos4A)) = 2 cos A

Answer 1

Answer:

√{2+√(2+2cos4A)}

=√[2+√{2+2(2cos²2A-1)}]

=√{2+√(2+4cos²2A-2)}

=√(2+√4cos²2A)

=√(2+2cos2A)

=√{2+2(2cos²A-1)}

=√(2+4cos²A-2)

=√4cos²A

=2cosA(Proved)