1)
2(cos \frac{ \pi }{8} +sin \frac{ \pi }{8} )^2=2(cos^2 \frac{ \pi }{8} +sin^2 \frac{ \pi }{8}+2cos \frac{ \pi }{8} *sin \frac{ \pi }{8})=2(1+sin \frac{ \pi }{4})= =2+2* \frac{ \sqrt{2} }{2}=2+ \sqrt{2}
2)
sin \pi *cos \frac{ \pi }{5}+4cos \frac{ \pi }{3} *sin \frac{5 \pi }{2} =0 *cos \frac{ \pi }{5}+4* \frac{1}{2} *sin \frac{ \pi }{2} =4* \frac{1}{2} *1 =2