[tex]RTP: \frac{1 + cos(2A)}{cos(2A)} = \frac{tan(2A)}{tan(A)}[/tex]
[tex]LHS = \frac{1 + cos(2A)}{cos(2A)}[/tex]
[tex]= \frac{1 + \frac{1 - tan^{2}(A)}{1 + tan^{2}(A)}}{\frac{1 - tan^{2}(A)}{1 + tan^{2}(A)}}[/tex]
[tex]= \frac{\frac{1 + tan^{2}(A) + 1 - tan^{2}(A)}{1 + tan^{2}(A)}}{\frac{1 - tan^{2}(A)}{1 + tan^{2}(A)}}[/tex]
[tex]= \frac{2}{1 - tan^{2}(A)}[/tex]
[tex]= \frac{2}{1 - tan^{2}(A)} \cdot \frac{tan(A)}{tan(A)}[/tex]
[tex]= \frac{\frac{2tan(A)}{1 - tan^{2}(A)}}{tan(A)}[/tex]
[tex]= \frac{tan(2A)}{tan(A)}[/tex]
[tex]= RHS[/tex], as required.
