lim(x→π/2) (tanx)^cosx=lim(x→π/2) e^[ln(tanx)^cosx]=lim(x→π/2) e^[ln(tanx)*cosx]=lim(x→π/2) e^[ln(tanx)/secx]=lim(x→π/2) e^[sec^2x/(tanx*secx*tanx)]=lim(x→π/2) e^[1/(tanx*cosx*tanx)]=lim(x...