[tex]A=\frac{2cos\frac{5a}{2}.sin\frac{a}{2}+2sin\frac{5a}{2}.cos\frac{5a}{2}}{cosa+cos4a}=\frac{2cos\frac{5a}{2}(sin\frac{a}{2}+sin\frac{5a}{2})}{2cos\frac{5a}{2}.cos\frac{3a}{2}}=\frac{2sin\frac{3a}{2}.cosa}{cos\frac{3a}{2}}=2tan\frac{3a}{2}.cosa[/tex]