If \[\int_{0}^{\pi }{x\,f({{\cos }^{2}}x+{{\tan }^{4}}x)\,dx}\] \[=k\int_{0}^{\pi /2}{f({{\cos }^{2}}x+{{\tan }^{4}}x)\,dx,}\] then the value of \[k\] is

• A.                 \[\frac{\pi }{2}\]              
• B.                 \[\pi \]
• C.                 \[-\frac{\pi }{2}\]             
• D.                 None of these